Conditional Probability

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Chapter 4.3

• Conditional Probability

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Intro to Venn diagrams - Pets
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Union, intersection, compliment
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Conditional probability

• The probability that the second event B occurs
  given that the first event A has occurred can be
  found by dividing the probability that both
  events occurred by the probability that the first
  event has occurred.
• P(BA)

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Selecting colored chips

• A box contains black chips and white chips. A
  person selects two chips without replacement. The
  probability of selecting a black chip and a white
  chip is 15/56, and the probability of selecting a
  black chip on the first draw is 3/8.
• How many chips are there?
• Create a Venn Diagram to represent the
  probabilities
• Find the probability of selecting two white chips
• Find the probability of selecting the white chip
  on the second draw, given that the first chip
  selected was a black chip.

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College courses

• At a large university, the probability that a
  student takes calculus and is on the deans list
  is 0.042. The probability that a student is on
  the deans list is 0.21. Find the probability
  that the student is taking calculus, given that
  he or she is on the deans list.

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Parking tickets

• The probability that Sam parks in a no-park zone
  and gets a parking ticket is 0.06, and the
  probability that Sam cannot find a legal parking
  space and has to park in the no-parking zone is
  0.20. On Tuesday, Sam arrives at school and has
  to park in the no-parking zone. Find the
  probability that he will get a parking ticket.

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Survey on women in the military

• A recent survey asked 100 people if they thought
  women in the armed forces should be permitted to
  participate in combat. The results of the survey
  are shown. Find the following probabilities
• The respondent answered yes, given that the
  respondent was a female
• The respondent was a male, given that the
  respondent answered no

Gender Yes No Total
Male 32 18 50
Female 8 42 50
Total 40 60 100
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At Least Probabilities Drawing Cards

• A game is played by drawing 4 cards from an
  ordinary deck and replacing each card after it is
  drawn. Find the probability that at least 1 ace
  is drawn.

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Tossing coins

• A coin is tossed 5 times Find the probability of
  getting at least 1 tail.

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Formal attire

• The Neckware Association of America reported that
  3 of ties sold in the U.S. are bow ties. If 4
  customers who purchased a tie are randomly
  selected, find the probability that at least 1
  selected a bow tie.

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Applying the concepts

• Pg. 228 1-8