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Birthday Problem

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, __) L1:SortA(L1) This will sort the day in increasing order; scroll through the list to see duplicate birthdays. Repeat many times.

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Birthday Problem

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  1. 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, __)L1:SortA(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))

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

  3. The union of a collection of events: The Additional Rule of Disjoint Events:

  4. General Addition Rule for Unions of 2 Events: • If events A and B are _________________, they can occur simultaneously. • Outcomes in common!

  5. 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 junior or a female • a senior or a female • not a junior male

  6. Example 6.23, p. 438 • Deborah guesses that the prob. of making partner in the firm is 0.7 and that Matthew’s is 0.5. She guesses that the prob. that both make partner is 0.3. • 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).

  7. Let A = the woman chosen is 18-29 • Let B = the woman is married Find: • P(A) 2) P(A and B) 3) P(B given A)

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

  9. 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.

  10. 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 purchaser 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?

  11. 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 didn’t get the extended warranty?

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