Examples Conditional Probability

1
Examples (Conditional Probability)

• Example 6
• 52 of the students at a certain college are
  females. 5 of the students in this college are
  majoring in computer science (CS). 2 of the
  students are women majoring in CS. If a student
  is selected at random, find the probability that
• this student is male who is not majoring in CS
• this student is female, given that the student is
  majoring in CS
• this student is majoring in CS, given that the
  student is female.

2

• Example 7
• In a certain community, 36 of families own a
  dog, and 22 of the families that own a dog also
  own a cat. In addition, 30 of the families own a
  cat. What is the probability that a randomly
  selected family
• owns neither a dog nor a cat?
• owns a dog, given that it owns a cat?

3

• Page104/3.10
• Suppose that a survey of married couples in a
  certain city shows that 20 of the husbands
  watched the 2003 Superbowl football game and 8
  of the wives. Also, if the husband watched, then
  the probability that the wife watched increased
  to 25. Find the probabilities of the following
  events
• The couple both watched
• At least one watched
• Neither watched
• The husband watched given that the wife watched

4

• Page104/3.12
• A company makes optical lenses under contract to
  the U.S. military. The lenses are ground to
  precise specifications and are shipped in lots of
  100. Military inspectors check 2 different lenses
  out of each lot of 100. Let E1 be the event that
  the first lens inspected fails inspection and E2
  be the event that the second fails. If either one
  of the two fails, then the entire shipment of 100
  lenses is returned. Suppose that 3 lenses in the
  shipment are bad. Find the probability that the
  shipment is rejected.