9.7 Probability of 9.7 Probability of Multiple EventsMultiple Events

Dependent events – when the Dependent events – when the outcome of one event affects the outcome of one event affects the outcome of a second eventoutcome of a second event

Independent events – when the Independent events – when the outcome of one event does outcome of one event does notnot affect affect the outcome of the second eventthe outcome of the second event

Ex 1Ex 1Classify as dependent or independentClassify as dependent or independent

Spin a spinner. Then, select a Spin a spinner. Then, select a marble from a bag that contains marble from a bag that contains marbles of different colors.marbles of different colors.

Select a marble from a bag that Select a marble from a bag that contains marbles of two colors. Put contains marbles of two colors. Put the marble aside, and select a the marble aside, and select a second marble from the bag.second marble from the bag.

What if we put the marble back???What if we put the marble back???

Probability of A and BProbability of A and B

If A and B are independent events, If A and B are independent events,

then P(A and B) = P(A)P(B)then P(A and B) = P(A)P(B)

Ex 2Ex 2

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

Mutually exclusive events – when two Mutually exclusive events – when two events cannot happen at the same events cannot happen at the same time. time.

If A and B are mutually exclusive If A and B are mutually exclusive events, then P(A and B) = 0.events, then P(A and B) = 0.

Ex 3Ex 3Are the events mutually exclusive?Are the events mutually exclusive?

Rolling an even number and rolling a Rolling an even number and rolling a number greater than 5 on a number number greater than 5 on a number cube?cube?

Rolling a prime number and a Rolling a prime number and a multiple of 6 on a number cube?multiple of 6 on a number cube?

Rolling an even number and rolling a Rolling an even number and rolling a number less than 2 on a number number less than 2 on a number cube.cube.

Probability of A or BProbability of A or B

If A & B are mutually exclusive events, If A & B are mutually exclusive events, then P(A or B) = P(A) + P(B)then P(A or B) = P(A) + P(B)

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

Ex 4Ex 4

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

Ex 5Ex 5

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

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

Ex 7Ex 7

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

Ex 8Ex 8P(5 or Jack)P(5 or Jack)

Ex 9Ex 9P(king or spade)P(king or spade)

Ex 10Ex 10

P(both red or both queens) if 2 cards P(both red or both queens) if 2 cards are drawn without replacementare drawn without replacement

Ex 11Ex 11

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