Birthday Problem

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Birthday Problem

• The probability of 2 people having the same
  birthday in a room of 41 people is 90.
• To randomly select ___ birthdays, randInt (1,
  365, __)?L1SortA(L1)
• This will sort the day in increasing order
  scroll through the list to see duplicate
  birthdays. Repeat many times.
• The following short program can be used to find
  the probability of at least 2 people in a group
  of n people having the same birthday
• Prompt N
• 1- (prod((seq((366-X)/365, X, 1, N, 1))

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• A couple plans to have three children. Find the
  probability that the children are
• (a) all boys
• (b) all girls
• (c) exactly two boys or exactly two girls
• (d) at least one child of each sex.

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• If events A and B are not disjoint, they can
  occur simultaneously.
• Outcomes in common!

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• In a statistics class there are 18 juniors and 10
  seniors 6 of the seniors are females, and 12 of
  the juniors are males. If a student is selected
  at random, find the probability of selecting
• (a) a junior or a female
• (b) a senior or a female
• (c) not a junior male

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Example 6.23, p. 438

• Deborah guesses that the prob. of making partner
  in the firm is 0.7 and that Matthews is 0.5. She
  guesses that the prob. that both make partner is
  0.3.
• 1) Find P(at least one is made partner)
• 2) P(neither is made partner)
• 3) P(Deborah makes partner and Matthew does not)
• 3) P(Matthew makes partner and Deborah does
  not).

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• Let A the woman chosen is 18-29
• Let B the woman is married
• 1) P(A)
• 2) P(A and B)
• 3) P(B given A)

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• The probability we assign to an event if we know
  that some other event has occurred.

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• Call a household prosperous if its income exceeds
  100,000. Call the household educated if the
  householder completed college. Select an American
  household at random, and let A be the event that
  the selected household is prosperous and B the
  event that it is educated. According to the
  Current Population Survey, P(A) 0.138, P(B)
  0.261, and the probability that a household is
  both prosperous and educated is P(A and B)
  0.082.
• What is the conditional probability that the
  household selected is prosperous given that it is
  educated?
• Are A and B independent? Use both methods of
  determining whether or not two events are
  independent.

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• Seventy-five percent of people who purchase hair
  dryers are women. Of these women purchases of
  hair dryers, thirty percent are over 50 years
  old. What is the probability that a randomly
  selected hair dryer purchases is a woman over 50
  years old?
• An insurance agent knows that 70 percent of her
  customers carry adequate collision coverage. She
  also knows that of those who carry adequate
  coverage, 5 percent have been involved in
  accidents and of those who do not carry adequate
  coverage, 12 percent have been involved in
  accidents. If one of her clients gets involved in
  an accident, then what is the probability that
  the client does not have adequate coverage?

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• 70 of people buy Brand 1 DVD player. 30 buy
  Brand 2. Of those who buy a DVD player, 20 of
  those who buy Brand 1 also get the extended
  warranty and 40 of those who buy Brand 2 get it.
  Make a tree diagram and then find the following
• What is the probability that they got Brand 1 and
  the extended warranty?
• What is the probability that they got Brand 2 and
  no extended warranty?
• What is the probability that they bought brand 2
  if they got the extended warranty?
• What is the probability they bought Brand 1 if
  they didnt get the extended warranty?