Independent and Dependent Events

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Independent and Dependent Events
Section 2
2
Vocabulary

• dependent events events where the outcome of the
  first event affects the outcome of the second
  event
• Be aware that numbers may decrease if an item is
  NOT replaced

3
Vocabulary

• independent events events where the outcome of
  one event does not affect the outcome of the
  other event (letters chosen to be on a license
  plate are independent)
• written as P(A and B) or sometimes P(A, then B)
• P (A and B) P(A) P(B)

4
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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sample space all possible outcomes of an
experiment

• Ex 2
• A baseball team has 8 pitchers and 3 catchers.
  The manager is choosing a pitcher-catcher
  combination. How many possibilities are there?

6
Ex 3

• A sandwich menu offers customers a choice of
  white, wheat or rye bread with one meat choice of
  ham, turkey, roast beef, chicken or salami. How
  many different combinations of bread and meat are
  possible?

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Ex 4

• An answering machine allows owners to call home
  and get their messages by entering a 3-digit
  code. How many codes are possible?
• How many codes would be possible if it was a
  4-digit code?

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Ex 5

• Joe wants to take 6 different classes next year.
  Assuming that each class is offered each period,
  how many different schedules could he have?
• How many different schedules could a student have
  who is planning to take only 4 different classes?

9
Ex 6

• A bag contains 3 white softballs, 2 yellow
  softballs, 3 green softballs, and 4 red
  softballs. You draw a ball without looking. You
  replace it and draw another ball. Find the
  probability that the first ball is red and the
  second ball is white.

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Ex 7

• 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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Ex 8

• A bag contains 3 green marbles, 2 red marbles, 4
  yellow marbles, and 1 black marble. Two are taken
  at random without replacement.
• Find P (green, then red).

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Ex 9

• A bag contains 3 green marbles, 2 red marbles, 4
  yellow marbles, and 1 black marble. Two are taken
  at random without replacement.
• Find P (green, then green).