Questions of basic probability for aptitude test
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5 DECEMBER 09 www.afterschool.tk 1
Questions of Basic Probability for
Aptitude Test
by :
DR. T.K. JAIN
AFTERSCHO☺OL
centre for social entrepreneurship
sivakamu veterinary hospital road
bikaner 334001 rajasthan, india
FOR – CSE & PGPSE STUDENTS
(CSE & PGPSE are free online programmes
open for all, free for all)
mobile : 91+9414430763
Questions of Basic Probability for
Aptitude Test
by :
DR. T.K. JAIN
AFTERSCHO☺OL
centre for social entrepreneurship
sivakamu veterinary hospital road
bikaner 334001 rajasthan, india
FOR – CSE & PGPSE STUDENTS
(CSE & PGPSE are free online programmes
open for all, free for all)
mobile : 91+9414430763
5 DECEMBER 09 www.afterschool.tk 2
My words.....
My purpose here is to give a few questions, which are
often asked in aptitude tests and competitive
examinations. Please prepare well for your examinations.
Please pass this presentation to all those who might need
it. Let us spread knowledge as widely as possible. I
welcome your suggestions. I also request you to help me
in spreading social entrepreneurship across the globe – for
which I need support of you people – not of any VIP.
With your help, I can spread the ideas – for which we
stand....
My words.....
My purpose here is to give a few questions, which are
often asked in aptitude tests and competitive
examinations. Please prepare well for your examinations.
Please pass this presentation to all those who might need
it. Let us spread knowledge as widely as possible. I
welcome your suggestions. I also request you to help me
in spreading social entrepreneurship across the globe – for
which I need support of you people – not of any VIP.
With your help, I can spread the ideas – for which we
stand....
5 DECEMBER 09 www.afterschool.tk 3
An biased die is tossed.Find the
probability of getting a
multiple of 3?
The possible options are : 1 to 6.
there are only 2 multiples of 3 : 3,6
so probability is (number of favourable
outcomes ) / (total number of possibilities)
= 2/6 = 1/3 answer
An biased die is tossed.Find the
probability of getting a
multiple of 3?
The possible options are : 1 to 6.
there are only 2 multiples of 3 : 3,6
so probability is (number of favourable
outcomes ) / (total number of possibilities)
= 2/6 = 1/3 answer
5 DECEMBER 09 www.afterschool.tk 4
In a simultaneous throw of a pair
of dice,find the
probability of getting a total more
than 7?
We can have 36 possibilities (6*6) however, we need only
those cases where the total is 8 or more. These are : (6,2),(6,3),
(6,4),(6,5),(6,6),(5,3),(5,4),(5,5),(5,6),(4,4),(4,5),(4,6),(3,5),
(3,6),(2,6) =15
answer = 15/36 = 5/12 answer
In a simultaneous throw of a pair
of dice,find the
probability of getting a total more
than 7?
We can have 36 possibilities (6*6) however, we need only
those cases where the total is 8 or more. These are : (6,2),(6,3),
(6,4),(6,5),(6,6),(5,3),(5,4),(5,5),(5,6),(4,4),(4,5),(4,6),(3,5),
(3,6),(2,6) =15
answer = 15/36 = 5/12 answer
5 DECEMBER 09 www.afterschool.tk 5
A bag contains 6 white and 4
black balls .Two balls are
drawn at random .Find the
probability that they are of the
same colour?
Both are white : 6/10*5/9
both are black = 4/10*3/9
add them : =42/90 or 7/15
or : 6c2/10C2*1/2 + 4c2/10c2
=21/45 = 7/15 answer
A bag contains 6 white and 4
black balls .Two balls are
drawn at random .Find the
probability that they are of the
same colour?
Both are white : 6/10*5/9
both are black = 4/10*3/9
add them : =42/90 or 7/15
or : 6c2/10C2*1/2 + 4c2/10c2
=21/45 = 7/15 answer
5 DECEMBER 09 www.afterschool.tk 6
Two dice are thrown
together.What is the probability
that the sum of the number on
the two faces is divisible by 4 or
6?
The possibilities are : (1,3)(1,5) (2,2) (2,4),(2,6),(3,1),(3,3),
(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)
thus we are able to get 14 out of 36. so answer = 7/18 answer
Two dice are thrown
together.What is the probability
that the sum of the number on
the two faces is divisible by 4 or
6?
The possibilities are : (1,3)(1,5) (2,2) (2,4),(2,6),(3,1),(3,3),
(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)
thus we are able to get 14 out of 36. so answer = 7/18 answer
5 DECEMBER 09 www.afterschool.tk 7
Two cards are drawn at random
from a pack of 52 cards What
is the probability that either both
are black or both are
queens?
Both are black = 26/52 * 25/51=25/102
both are queens : 4/52 * 3/51=3/663
both are black queens : 2/52*1/51 = 1/1326
now add them : (25/102 + 3/663 – 1/1326)
=(325+6-1)/1326
=330/1326 or .25 answer
Two cards are drawn at random
from a pack of 52 cards What
is the probability that either both
are black or both are
queens?
Both are black = 26/52 * 25/51=25/102
both are queens : 4/52 * 3/51=3/663
both are black queens : 2/52*1/51 = 1/1326
now add them : (25/102 + 3/663 – 1/1326)
=(325+6-1)/1326
=330/1326 or .25 answer
5 DECEMBER 09 www.afterschool.tk 8
Two dices are tossed the
probability that the total score
is a prime number?
Prime numbers are : 1,2,3,5,7,11
totals are : (1,2),(1,1),(1,4),(1,6),(2,1),(2,3),
(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),6,1),(6,5)
=15/36 answer
Two dices are tossed the
probability that the total score
is a prime number?
Prime numbers are : 1,2,3,5,7,11
totals are : (1,2),(1,1),(1,4),(1,6),(2,1),(2,3),
(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),6,1),(6,5)
=15/36 answer
5 DECEMBER 09 www.afterschool.tk 9
Two dice are thrown simultaneously .what is
the probability
of getting two numbers whose product is even?
If any one of the two numbers is an even number, the
product will be even number. Thus we should pick up all
those cases when both the numbers are odd numbers :
(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3) (5,5)
thus there are only 9 such cases. Remove them from 36,
we get : 27 cases
answer : 27/36 answer
Two dice are thrown simultaneously .what is
the probability
of getting two numbers whose product is even?
If any one of the two numbers is an even number, the
product will be even number. Thus we should pick up all
those cases when both the numbers are odd numbers :
(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3) (5,5)
thus there are only 9 such cases. Remove them from 36,
we get : 27 cases
answer : 27/36 answer
5 DECEMBER 09 www.afterschool.tk 10
In a lottery ,there are 10 prizes and 25 blanks.A
lottery is
drawn at random. what is the probability of
getting a prize ?
10/(10+25)
=10/35 or 2/7 answer
In a lottery ,there are 10 prizes and 25 blanks.A
lottery is
drawn at random. what is the probability of
getting a prize ?
10/(10+25)
=10/35 or 2/7 answer
5 DECEMBER 09 www.afterschool.tk 11
In a class ,30 % of the students offered English,20 %
offered Hindi and 10 %offered Both.If a student is
offered at random, what is the probability that he has
offered English or Hindi?
30+20-10 = 40% or .4 answer
In a class ,30 % of the students offered English,20 %
offered Hindi and 10 %offered Both.If a student is
offered at random, what is the probability that he has
offered English or Hindi?
30+20-10 = 40% or .4 answer
5 DECEMBER 09 www.afterschool.tk 12
Two cards are drawn from a pack of 52 cards .What is
the probability that either both are Red or both are
Kings?
Both are red ½ * 25/51
both are king = 4/52 + 3/51
now add both these answers =55/221
Two cards are drawn from a pack of 52 cards .What is
the probability that either both are Red or both are
Kings?
Both are red ½ * 25/51
both are king = 4/52 + 3/51
now add both these answers =55/221
5 DECEMBER 09 www.afterschool.tk 13
one card is drawn at random from a pack of 52 cards.What
is the probability that the card drawn is a face card?
Face cards are : Jack, queen, king
total = 12
12/52 answer
one card is drawn at random from a pack of 52 cards.What
is the probability that the card drawn is a face card?
Face cards are : Jack, queen, king
total = 12
12/52 answer
5 DECEMBER 09 www.afterschool.tk 14
A man and his wife appear in an interview for two
vacancies in the same post.The probability of husband's
selection is 1/7 and the probabililty of wife's selection is
1/5.What is the probabililty that only one of them is
selected?
Husband + not wife
=1/7 * 4/5 = 4/35
wife + not husband
=1/5 * 6/7 = 6/35
add = 10/35 answer
A man and his wife appear in an interview for two
vacancies in the same post.The probability of husband's
selection is 1/7 and the probabililty of wife's selection is
1/5.What is the probabililty that only one of them is
selected?
Husband + not wife
=1/7 * 4/5 = 4/35
wife + not husband
=1/5 * 6/7 = 6/35
add = 10/35 answer
5 DECEMBER 09 www.afterschool.tk 15
From a pack of 52 cards,one card is drawn at
random.What is the probability that the card is
a 10 or a spade?
4/52 + 13/52 – 1/52
=16/52 answer
From a pack of 52 cards,one card is drawn at
random.What is the probability that the card is
a 10 or a spade?
4/52 + 13/52 – 1/52
=16/52 answer
5 DECEMBER 09 www.afterschool.tk 16
A bag contains 4 white balls ,5 red and 6 blue balls .Three
balls are drawn at random from the bag.What is the
probability that all of them are red ?
5/15*4/14*3/13
or 5c2/15c2 =
=2/91
A bag contains 4 white balls ,5 red and 6 blue balls .Three
balls are drawn at random from the bag.What is the
probability that all of them are red ?
5/15*4/14*3/13
or 5c2/15c2 =
=2/91
5 DECEMBER 09 www.afterschool.tk 17
A box contains 10 block and 10 white balls.What is
the probability of drawing two balls of the same
colour?
Both are black :
10/20 * 9/19 =9/38
+both are white :
10/20 * 9/19 =9/38
or
black : 10c2 / 20c2
+white : 10c2 / 20c 2
=90/190
A box contains 10 block and 10 white balls.What is
the probability of drawing two balls of the same
colour?
Both are black :
10/20 * 9/19 =9/38
+both are white :
10/20 * 9/19 =9/38
or
black : 10c2 / 20c2
+white : 10c2 / 20c 2
=90/190
5 DECEMBER 09 www.afterschool.tk 18
A box contains 20 electricbulbs ,out of which 4 are
defective, two bulbs are chosen at random from this
box.What is the probability that at least one of these is
defective ?
In such questions (at least one type), it is better
to reverse the question, solve it and deduct the
answer from 1. So here we shall first calculate
the probability of getting no defective bulb.
Let us assume that no bulb is defective :
16/20 * 15/19 = 12/19
at least one is defective = 1 -12/19
= 7/19 answer
A box contains 20 electricbulbs ,out of which 4 are
defective, two bulbs are chosen at random from this
box.What is the probability that at least one of these is
defective ?
In such questions (at least one type), it is better
to reverse the question, solve it and deduct the
answer from 1. So here we shall first calculate
the probability of getting no defective bulb.
Let us assume that no bulb is defective :
16/20 * 15/19 = 12/19
at least one is defective = 1 -12/19
= 7/19 answer
5 DECEMBER 09 www.afterschool.tk 19
Two cards are drawn together
from apack of 52 cards.What is
the probability that
one is a spade and one is a heart ?
First is spade and 2
nd
heart :
13/52 * 13/51 = 13/204
First is heart and 2
nd
spade :
13/52 * 13/51 = 13/204
add them : 13/102 answer
Two cards are drawn together
from apack of 52 cards.What is
the probability that
one is a spade and one is a heart ?
First is spade and 2
nd
heart :
13/52 * 13/51 = 13/204
First is heart and 2
nd
spade :
13/52 * 13/51 = 13/204
add them : 13/102 answer
5 DECEMBER 09 www.afterschool.tk 20
The probability that a card drawn
from a pack of 52 cards will be a
diamond or a king?
13/52 + 4/52 – 1/52
=16/52
The probability that a card drawn
from a pack of 52 cards will be a
diamond or a king?
13/52 + 4/52 – 1/52
=16/52
5 DECEMBER 09 www.afterschool.tk 21
Download more resources
http://www.esnips.com/web/onlinespeeches
Download more resources
http://www.esnips.com/web/onlinespeeches
5 DECEMBER 09 www.afterschool.tk 22
http://www.esnips.com/doc/a4161e7a-6859-4583-b3b9-fc8883819ca2/REASONING-QUIZ
http://www.esnips.com/doc/292f3066-dfff-4507-9ef8-f07991c83ca6/reasoning-made-simple
http://www.esnips.com/doc/61098141-2b35-4dd2-8c71-a26c481e4406/25-JULY-REASONING--DI
http://www.esnips.com/doc/6335a093-fa8b-4829-91b7-99614c3b36b4/16-July-Reasoning-I
http://www.esnips.com/doc/17998a15-f26a-4de7-b8a7-2b964fcde13f/Logic-and-Reasoning
http://www.esnips.com/doc/816ec880-c1d5-436c-b5f3-d05525416f0e/1-AUGUST-Reasoning--DI
http://www.esnips.com/doc/026362a7-efe4-42ef-afe2-1cf7c672d11f/17-reasoning-II
http://www.esnips.com/doc/ebceaf38-3af0-4b62-bd4a-1a9c1b002d47/reasoning-15-may
http://www.esnips.com/doc/a4161e7a-6859-4583-b3b9-fc8883819ca2/REASONING-QUIZ
http://www.esnips.com/doc/292f3066-dfff-4507-9ef8-f07991c83ca6/reasoning-made-simple
http://www.esnips.com/doc/61098141-2b35-4dd2-8c71-a26c481e4406/25-JULY-REASONING--DI
http://www.esnips.com/doc/6335a093-fa8b-4829-91b7-99614c3b36b4/16-July-Reasoning-I
http://www.esnips.com/doc/17998a15-f26a-4de7-b8a7-2b964fcde13f/Logic-and-Reasoning
http://www.esnips.com/doc/816ec880-c1d5-436c-b5f3-d05525416f0e/1-AUGUST-Reasoning--DI
http://www.esnips.com/doc/026362a7-efe4-42ef-afe2-1cf7c672d11f/17-reasoning-II
http://www.esnips.com/doc/ebceaf38-3af0-4b62-bd4a-1a9c1b002d47/reasoning-15-may
5 DECEMBER 09 www.afterschool.tk 23
Download links ....
http://www.esnips.com/doc/1ca22536-6475-4fa4-bb7f-5f77757301a1/30-may-reasoning
http://www.esnips.com/doc/3e7518ef-dc30-4309-af0f-8dd63ec028db/16-July-Reasoning-I
http://www.esnips.com/doc/f5f8334d-7642-4154-9bfa-96eee4527798/11-July-Reasoning-II
http://www.esnips.com/doc/caf3db9b-7739-4f37-86a3-1fd675702b64/11-July-Reasoning
http://www.esnips.com/doc/ebceaf38-3af0-4b62-bd4a-1a9c1b002d47/reasoning-15-may
http://www.esnips.com/doc/3aab1a3a-43f3-49a8-b819-af47124d2382/19-JUNE-REASONING--DI
Download links ....
http://www.esnips.com/doc/1ca22536-6475-4fa4-bb7f-5f77757301a1/30-may-reasoning
http://www.esnips.com/doc/3e7518ef-dc30-4309-af0f-8dd63ec028db/16-July-Reasoning-I
http://www.esnips.com/doc/f5f8334d-7642-4154-9bfa-96eee4527798/11-July-Reasoning-II
http://www.esnips.com/doc/caf3db9b-7739-4f37-86a3-1fd675702b64/11-July-Reasoning
http://www.esnips.com/doc/ebceaf38-3af0-4b62-bd4a-1a9c1b002d47/reasoning-15-may
http://www.esnips.com/doc/3aab1a3a-43f3-49a8-b819-af47124d2382/19-JUNE-REASONING--DI
5 DECEMBER 09 www.afterschool.tk 24
Download links...
http://www.esnips.com/doc/8f6897b7-0bab-4e53-858a-697bf192fd7b/reasoning-and-DI-12-September
http://www.esnips.com/doc/23aac52e-3ecf-4d89-8b69-57d3fed77fd2/4-june-reasoning
http://www.esnips.com/doc/48840095-2865-4eb1-8810-e818aacd1e25/4-JULY-Reasoning--DI
http://www.esnips.com/doc/67a0ff61-c31f-43a0-9941-49a17b15c8c3/3-JULY--Reasoning--DI
http://www.esnips.com/doc/f6d85f1b-881b-4e93-8341-8c779e98868d/1-AUGUST-Reasoning--DI
Download links...
http://www.esnips.com/doc/8f6897b7-0bab-4e53-858a-697bf192fd7b/reasoning-and-DI-12-September
http://www.esnips.com/doc/23aac52e-3ecf-4d89-8b69-57d3fed77fd2/4-june-reasoning
http://www.esnips.com/doc/48840095-2865-4eb1-8810-e818aacd1e25/4-JULY-Reasoning--DI
http://www.esnips.com/doc/67a0ff61-c31f-43a0-9941-49a17b15c8c3/3-JULY--Reasoning--DI
http://www.esnips.com/doc/f6d85f1b-881b-4e93-8341-8c779e98868d/1-AUGUST-Reasoning--DI
5 DECEMBER 09 www.afterschool.tk 25
Download links...
http://www.slideshare.net/tkjainbkn/reasoning
http://www.slideshare.net/tkjainbkn/reasoning-2814907
http://www.scribd.com/doc/28677498/
Download links...
http://www.slideshare.net/tkjainbkn/reasoning
http://www.slideshare.net/tkjainbkn/reasoning-2814907
http://www.scribd.com/doc/28677498/
5 DECEMBER 09 www.afterschool.tk 26
Download links....
http://www.scribd.com/doc/28617263/Syllabus-of-Mat-Rmat-Cet-2010
http://www.scribd.com/doc/28617157/Vedic-Mathematics-for-All
http://www.scribd.com/doc/28616660/English-Improvement-for-Competitive-Examinations-and-Aptitude-Tests
http://www.scribd.com/doc/28531795/Mock-Paper-Cat-Rmat-Mat-Sbi-Bank-Po-Aptitude-Tests
http://www.scribd.com/doc/23610071/Reasoning
http://www.scribd.com/doc/14675645/10-July-Reasoning-II
http://www.scribd.com/doc/23393680/REASONING-AFTERSCHOOOL
http://www.scribd.com/doc/6583303/Reasoning-Afterschoool
Download links....
http://www.scribd.com/doc/28617263/Syllabus-of-Mat-Rmat-Cet-2010
http://www.scribd.com/doc/28617157/Vedic-Mathematics-for-All
http://www.scribd.com/doc/28616660/English-Improvement-for-Competitive-Examinations-and-Aptitude-Tests
http://www.scribd.com/doc/28531795/Mock-Paper-Cat-Rmat-Mat-Sbi-Bank-Po-Aptitude-Tests
http://www.scribd.com/doc/23610071/Reasoning
http://www.scribd.com/doc/14675645/10-July-Reasoning-II
http://www.scribd.com/doc/23393680/REASONING-AFTERSCHOOOL
http://www.scribd.com/doc/6583303/Reasoning-Afterschoool
5 DECEMBER 09 www.afterschool.tk 27
Download links for material in english
http://www.authorstream.com/presentation/tkjainbkn-146799-english-error-spotting-sentence-im-law-cat-gmat-mba-management-business-research-cfp-cfa-frm-cpa-ca-cs-icwa-india-rajasthan-improvement-entertainment-ppt-powerpoint/
http://www.docstoc.com/docs/3921499/ENGLISH-%E2%80%93-ERROR-SPOTTING-AND-SENTENCE-IMPROVEMENT
http://www.slideshare.net/tkjainbkn/english-error-spotting-and-sentence-improvement-presentation
http://www.scribd.com/doc/19641980/Error-Spotting
http://www.scribd.com/doc/11629005/English-Error-Spotting-and-Sentence-Improvement
http://www.scribd.com/doc/14660441/English-Afterschoool-23-May
http://www.scribd.com/doc/6583519/English-Afterschoool-21-May
http://www.scribd.com/doc/6583520/English-Afterschoool-21-May-2
Download links for material in english
http://www.authorstream.com/presentation/tkjainbkn-146799-english-error-spotting-sentence-im-law-cat-gmat-mba-management-business-research-cfp-cfa-frm-cpa-ca-cs-icwa-india-rajasthan-improvement-entertainment-ppt-powerpoint/
http://www.docstoc.com/docs/3921499/ENGLISH-%E2%80%93-ERROR-SPOTTING-AND-SENTENCE-IMPROVEMENT
http://www.slideshare.net/tkjainbkn/english-error-spotting-and-sentence-improvement-presentation
http://www.scribd.com/doc/19641980/Error-Spotting
http://www.scribd.com/doc/11629005/English-Error-Spotting-and-Sentence-Improvement
http://www.scribd.com/doc/14660441/English-Afterschoool-23-May
http://www.scribd.com/doc/6583519/English-Afterschoool-21-May
http://www.scribd.com/doc/6583520/English-Afterschoool-21-May-2
5 DECEMBER 09 www.afterschool.tk 28
Download links for material on
English
http://www.scribd.com/doc/6583315/English-Improvement-Afterschoool
http://www.scribd.com/doc/6583518/English-20-May-Afterschoool
http://www.scribd.com/doc/28531795/Mock-Paper-Cat-Rmat-Mat-Sbi-Bank-Po-Aptitude-Tests
Download links for material on
English
http://www.scribd.com/doc/6583315/English-Improvement-Afterschoool
http://www.scribd.com/doc/6583518/English-20-May-Afterschoool
http://www.scribd.com/doc/28531795/Mock-Paper-Cat-Rmat-Mat-Sbi-Bank-Po-Aptitude-Tests
5 DECEMBER 09 www.afterschool.tk 29
Links
http://www.scribd.com/doc/14647398/English-Improvement-and-Word-Power
http://www.scribd.com/doc/14660508/General-Knowledge-24-May-3
http://www.scribd.com/doc/19628963/Mathematics
http://www.scribd.com/doc/19492878/Direct-and-Indirect-Speech-in-English
Links
http://www.scribd.com/doc/14647398/English-Improvement-and-Word-Power
http://www.scribd.com/doc/14660508/General-Knowledge-24-May-3
http://www.scribd.com/doc/19628963/Mathematics
http://www.scribd.com/doc/19492878/Direct-and-Indirect-Speech-in-English
5 DECEMBER 09 www.afterschool.tk 30
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5 DECEMBER 09 www.afterschool.tk 31
ADDITIONAL LINKS
http://www.scribd.com/doc/11692763/Advanced-Mathematics-for-GMAT-CAT-MAT
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http://www.scribd.com/doc/11625819/Basic-Mathematics-for-Cat-GMAT-Mat
http://www.scribd.com/doc/23407954/mathematics-for-OPENMAT-MAT-CAT-GMAT-25-april
http://www.scribd.com/doc/23407934/Advanced-Mathematics-for-GMAT-CAT-MAT2
http://www.scribd.com/doc/6583520/English-Afterschoool-21-May-2
http://www.scribd.com/doc/23300964/Advanced-Mathematics-for-GMAT-CAT-MAT2
http://www.scribd.com/doc/23407945/MATHEMATICS-FOR-ATMA-CAT-MAT-GMAT-BANK-PO-GRE
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http://www.scribd.com/doc/23407636/10-July-reasoning
http://www.scribd.com/doc/6583273/Reasoning-Quiz
http://www.scribd.com/doc/23393476/10-July-reasoning
http://www.scribd.com/doc/23393716/REASONING-QUIZ
http://www.scribd.com/doc/14705025/17-Reasoning-II
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