Question 1100907: Exercise 4
Given a standard deck of 52 playing cards, what is the probability of drawing four cards that form two different pairs. For example 2 queens and 2 tens, or 2 fives and 2 sevens. The pairs must be different from each other, four of the same kind does not qualify.
Exercise 5
The principal of a school wants to form a committee students to come up with a new dress code. She wants the committee to have 4 senior students, 3 junior students, and 2 sophomore student. If the school has 11 seniors, 15 juniors, and 19 sophomores, how many committees are possible?
Exercise 6
Two sources of name and date-of-birth data have been acquired and merged into a single file. In the combined file, 75% of the records came from Source A, and 25% of the records are from Source B. It is also true that the names are correct on 60% of records from Source A, and 90% of the records from Source B have a correct name. Based on this information, answer the following questions.
• If a record is randomly selected from the combined file, what is the probability that it originally came from Source B?
• If a record is randomly selected from the combined file, what is the probability that it will have a correct name?
• If a record is selected from the combined file and is found to have a correct name, what is the probability that the record came from Source A? (hint use Bayes Theorem where H = Probability record is from Source A, and D = The name is correct)
Exercise 7
Over time, a bank has found that on average there is a 2% chance that one of its loans will go into default for non-payment within the next 12 months. To try and reduce this risk, a data scientist at the bank has developed a “big data” screening test that looks at the payment history of a loan and predicts whether the loan will go into default in the next 12 months. When the test is applied to the payment history of loans that actually went into default, the test is positive 96% of the time. When test is applied to the payment history for loans that did not default, the test was negative 94% of the time. Use Bayes Theorem to answer the following question. If the new test is applied to an active loan at random and the test is positive, what is the probability the loan will go into default in the next 12 months?
Answer by ikleyn(52803)   (Show Source):
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