prob_solution.pdf - Solutions Probability Problem 1 Your...

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Solutions 1 Probability Problem 1: Your professor gives a surprise quiz consisting of 10 true/false questions. A) What is the complement of the event of getting at least one question wrong? Getting none of the questions wrong (i.e. getting all questions correct). B) With random guessing for each question, show that the probability of getting at least one question wrong is 0.999 Let event A = get at least one question wrong. P(A) = 1 P(A c ) = 1 P(get none wrong) P(A) = 1 0.5 10 = 1 0.001 = 0.999 Problem 2: Based on records of automobile accidents in a recent year, the Department of Highway Safety and Motor Vehicles in Florida reported the counts who survived (S) and died (D), according to whether they wore a seat belt (Y = yes, N = no). The data are presented in the table below. Outcome of accident Wore Seat Belt Survived (S) Died (D) Total Yes (Y) 412,368 510 412,878 No (N) 162,527 1601 164,128 Total 574,895 2111 577,006 A) Using these data, find P(D) and the P(N). P(D) = 2111/577,006 = 0.004 P(N) = 164,128 / 577,006 = 0.284 B) Find the probability that an individual did not wear a seat belt and died. That is, find P(N and D).
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