 # 9.7 Probability of Multiple Events. Dependent events – when the outcome of one event affects the outcome of a second event Dependent events – when the.

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9.7 Probability of Multiple Events

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

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???

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

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?

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.

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.

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)

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?

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?

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.

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?

Ex 8 P(5 or Jack)