INTRODUCTION TO PROBABILITY.pptx

Introducing Probability, it's terms and examples.

1. INTRODUCTION TO PROBABILITY DR. FARHANA SHAHEEN

2. PROBABILITY

3. Tossing a coin Rolling a dice Have two possibilities Have six possibilities Head or Tail Getting 1, 2, 3, 4, 5, 6

4. Spinning Wheel

5. Probability Line

6. Language of Probability

7. Terms used in Probability Certain Likely Equally likely Unlikely Impossible

8. Note: For an Event E to occur: Certain means 100% chances. Likely means more chances Unlikely means less chances Equally Likely means 50% chances Impossible means No chance at all ( 0 % chances)

9. Likely… More vs Less Likely

10. Exhaustive Events: In probability, a set of events is collectively exhaustive  if they cover all of the probability space : i.e., the probability of any one of them happening is 100%. If a set of statements is collectively exhaustive we know at least one of them is true.

11. Mutually Exclusive Events Disjoint events, events that don’t have anything in common. Non-Mutually Exclusive Events are also called Mutually Inclusive events. Mutually Exclusive Events:

12. Activity

13. PROBABILITY RULES P(E) = P( Not E) = 1 – P(E) For any event E, . P(E) = 0 if and only if E is an impossible event. i.e. it will Never occur. P(E) = 1 if and only if E is a certain event. i.e. it will Definitely occur  

14. Ques:01 A card is drawn at random from a standard pack of 52 playing cards. Find the probability of drawing : 1. E = a red card 2. E = an ace 3. E = the three of clubs (3 of club) 4. E = a card which is not the three of clubs

15. Ques:02 Two joker cards are added to a standard pack of 52 playing cards. A card is then drawn at random from the 54 cards. Find the probability of drawing ( i ) a red card (ii) a two (iii) a joker (iv) a queen or a king Note: A Joker card is neither a black or red card.

16. Ques:03 Raj wakes up in the morning and notices that his digital clock reads 07:25. (ST:AB) At noon, he looks at the clock again. What is the probability that ( i ) the number in column A is a 4? (ii) the number in column B is 8? (iii) the number in column A is less than 6. (iv) the number in column B is greater than 5?

17. Solution: A = {0, 1, 2, 3, 4, 5} B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} ( i ) the number in column A is a 4? P(E) = 1/6 (ii) the number in column B is 8? P(E) = 1/10 (iii) the number in column A is less than 6. P(E) = 6/6 = 1 (iv) the number in column B is greater than 5? P(E) = 4/10 = 2/5

18. Ques:04 There are a total 117 pairs of socks in a clothes bin. Each pair of socks is placed in a bag. The probabilities of selecting a yellow pair of socks and a grey pair of socks at random from the bin are 2/9 and 3/13 respectively. Find the number of pairs of socks in the bin which are ( i ) yellow, (ii) neither yellow nor grey.

19. Ques:05 A carton contains 15 toothbrushes, out of which p have soft bristles. After 5 more toothbrushes of soft bristles are added to the carton, the probability of drawing a toothbrush with soft bristles becomes ¾. Find the value of p.

20. Ques:06 There are 50 students in an Auditorium, of which 2x are boys and y are girls. After (y – 6) boys leave the Auditorium and (2x – 5) girls enter the Auditorium, the probability of selecting a girl at random becomes 9/13. Find the value of x and y.