9.7 Probability of Multiple Events

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9.7 Probability of Multiple Events
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• 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

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Ex 1Classify as dependent or independent

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

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Probability of A and B

• If A and B are independent events,
• then P(A and B) P(A)P(B)

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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?

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• 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.

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Ex 3Are the events mutually exclusive?

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

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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)

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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?

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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?

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Ex 6Find 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.
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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?

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Ex 8P(5 or Jack)
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Ex 9P(king or spade)
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Ex 10

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

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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).