Chapter 7 Review Problems

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Chapter 7 Review Problems
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Problem 1

• Use a Venn diagram and the given information to
  determine the number of elements in the indicated
  region.
• n(A) 35, n(B) 18, n(A ? B) 45, n(B?)
  43
• Find n(A ? B)?

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Problem 2

• Use a Venn diagram to find the indicated
  probability.
• P(R) 0.39, P(S) 0.34, P(R ? S) 0.21
• Find P(R? ? S)

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Problem 3

• A card is drawn from a well-shuffled deck of 52
  cards. What is the probability of drawing a red
  card that has a value greater than 5? (Assume
  Aces are high.)

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Problem 4

• The age distribution of students at a community
  college is given below.
• Age (years) Number of Students
• Under 21 525
• 21 25 509
• 26 30 322
• 31 35 115
• Over 35 87
• A student is selected at random. Find the
  probability that the student is at most 25 years
  old. Round to the nearest thousandth.

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Problem 5

• The odds in favor of a football team winning the
  Super Bowl are posted as 65. Find the
  probability that the team will lose the Super
  Bowl.

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Problem 6

• Assume that two gumballs are chosen from a bag of
  gumballs with 4 blue, 1 white, 3 green, and 3
  red. Find the probability that
• a.) both gumballs are blue.
• b.) the first gumball is red and the second
• gumball is green.

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Problem 7

• In a certain U.S. city, 54.9 of adults are
  women. In that city, 16.2 of women and 10.2 of
  men do not use any means of public
  transportation. If an adult is selected at
  random from the city, find the probability that
  the person does not use any form of public
  transportation.

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Problem 8

• A card is drawn from a well-shuffled deck of 52
  cards.
• Let A be the event that the card is a spade.
• Let B be the event that the card is a ten.
• Find P(A)
• P(B)
• P(A ? B)
• Are events A and B independent?
• How can you tell?

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Problem 9

• A person must select one of three bags, each
  filled with pennies. One bag contains a gold
  coin. The probability of bag A being selected is
  0.35, while the probability of bag B being
  selected is 0.28. The probability of finding a
  gold coin in bag A is 0.3,in bag B is 0.45, and
  in bag C is 0.8. A bag is selected at random.
• a.) Draw a tree diagram and label each branch
  with
• the appropriate probabilities.
• b.) What is the probability of getting the gold
  coin?
• c.) Given that a person got the gold coin, what
  is the
• probability that bag C contained the
  coin?

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Problem 10

• A survey of 200 families showed that 98 had a
  dog 57 had a cat 20 had a dog and a cat 51 had
  neither a dog nor a cat nor a parakeet and 2 had
  a cat, a dog, and a parakeet.
• How many families had a parakeet only?

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Answers

• 1.) 53
• 2.) 0.82
• 3.) 9/26 or 0.35
• 4.) 0.664
• 5.) 5/11
• 6.) a.) 6/55 or 0.1091 b.) 9/110 or 0.818
• 7.) 0.135
• 8.) P(A) ¼ P(B) 1/13
• P(A ? B) 1/52 Independent events
• Because P(A) P(B) P(A ? B)
• 9.) b.) 0.527 c.) 0.562
• 10.) 14