1. 9.7 Probability of Multiple Events

2. Dependent events – when the outcome of one event affects the outcome of a second event Dependent events – when the outcome of one event affects the outcome of a second event Independent events – when the outcome of one event does not affect the outcome of the second event Independent events – when the outcome of one event does not affect the outcome of the second event

3. Ex 1 Classify as dependent or independent Spin a spinner. Then, select a marble from a bag that contains marbles of different colors. Spin a spinner. Then, select a marble from a bag that contains marbles of different colors. Select a marble from a bag that contains marbles of two colors. Put the marble aside, and select a second marble from the bag. Select a marble from a bag that contains marbles of two colors. Put the marble aside, and select a second marble from the bag. What if we put the marble back??? What if we put the marble back???

4. Probability of A and B If A and B are independent events, then P(A and B) = P(A)P(B)

5. Ex 2 A box contains 20 red marbles and 30 blue marbles. A second box contains 10 white marbles and 47 black marbles. If you choose one marble from each box without looking, what is the probability that you get a blue marble and a black marble? A box contains 20 red marbles and 30 blue marbles. A second box contains 10 white marbles and 47 black marbles. If you choose one marble from each box without looking, what is the probability that you get a blue marble and a black marble?

6. Mutually exclusive events – when two events cannot happen at the same time. Mutually exclusive events – when two events cannot happen at the same time. If A and B are mutually exclusive events, then P(A and B) = 0. If A and B are mutually exclusive events, then P(A and B) = 0.

7. Ex 3 Are the events mutually exclusive? Rolling an even number and rolling a number greater than 5 on a number cube? Rolling an even number and rolling a number greater than 5 on a number cube? Rolling a prime number and a multiple of 6 on a number cube? Rolling a prime number and a multiple of 6 on a number cube? Rolling an even number and rolling a number less than 2 on a number cube. Rolling an even number and rolling a number less than 2 on a number cube.

8. Probability of A or B If A & B are mutually exclusive events, then P(A or B) = P(A) + P(B) If A & B are NOT mutually exclusive events, then P(A or B) = P(A) + P(B) – P(A and B)

9. Ex 4 At a restaurant, customers get to choose one of four vegetables with any main course. About 33% of the customers choose green beans, and about 28% choose spinach. What is the probability that a customer will choose beans or spinach?

10. Ex 5 A spinner has twenty equal size sections numbered from 1 to 20. If you spin the spinner, what is the probability that the number you spin will be a multiple of 2 or a multiple of 3?

11. Ex 6 Find the probability of selecting a boy or a blonde-haired person from 12 girls, 5 of whom have blonde hair, and 15 boys, 6 of whom have blonde hair.

12. Ex 7 A bank contains 4 nickels, 4 dimes and 7 quarters. Three coins are removed in sequence without replacement. What is the probability of selecting a nickel, a dime and a quarter in that order? A bank contains 4 nickels, 4 dimes and 7 quarters. Three coins are removed in sequence without replacement. What is the probability of selecting a nickel, a dime and a quarter in that order?

13. Ex 8 P(5 or Jack)

14. Ex 9 P(king or spade)

15. Ex 10 P(both red or both queens) if 2 cards are drawn without replacement P(both red or both queens) if 2 cards are drawn without replacement

16. Ex 11 There are 5 male and 5 female students. A committee of 4 members is to be selected at random. Find P(all female). There are 5 male and 5 female students. A committee of 4 members is to be selected at random. Find P(all female).