mutually and nonmutually event.pptx

math 10

1. Mutually Exclusive Events and Not Mutually Exclusive Events

2. Two events may or may not happen at the same time.

3. What is a Mutually Exclusive Event? - Events that do not have the same elements - Events that can’t happen at the same time

4. Example 1.Getting a 3 or getting a 2 in rolling a die.

5. 2. Getting a red card and a black card in a standard deck of cards

6. 3.A card is drawn from a deck of standard playing cards. Event A: An ace is drawn. Event B: A king is drawn.

7. 2. A rectangular box contains balls numbered {1, 2, 3, … , 18, 19, 20}. If a ball is randomly drawn from a box, a. what is the probability that it is 3 or 15? Solution: 1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,…20 P( A or B) = P( A ) + P( B) P( 3 or 15 ) = P( 3 ) + P( 15) = 1/20+ 1/20 P(3 or 15) = 2/20 or 1/10

8. Not Mutually Exclusive Events -Events that have outcomes in common.

9. Example: From a deck of 52 cards, what is the probability that the card is a face card or a black card?

10. A rectangular box contains balls numbered {1, 2, 3, … , 18, 19, 20}. If a ball is randomly drawn from a box, what is the probability that it is a number divisible by 4 or a number divisible by 5?   Solution: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 No. divisible by 4 – ( 4,8,12,16,20) No.divisible by 5 –( 5,10,15,20) P ( A or B) = P( A) + P ( B ) – P ( A and B) P(no. div.by 4 or no. div. by 5 ) = 5/20 + 4/20 – 1/20 = 8/20 P( no.div.by 4 or no.div.by 5 ) =2/5

11. Determine whether each of the following event is mutually exclusive or not mutually exclusive events. Then find its probability.   1. Getting a 6 or a number divisible by 3 when rolling a die 2 Getting 3 tails or 1 head when four coins are dropped onto the floor. 3. Selecting a blue or a red when picking a ball from a box that contains 10 blue balls and 15 red balls 4. Selecting a letter A from the word PROBABILITY or a vowel 5. Getting a head or a tail when tossing a coin