Question 2: [5 Poin An experiment results in one of five sample points with the

Question

Question 2: [5 Poin An experiment results in one of five sample points with the following probabilities: PE)0.22, PE) 0.31, PE)-0.15. PE)-0.22, PRE) 0. 1. The following events have been defined B: (E, E, Es), and C: (E1, Es) Use this infomation to find a. the probability of A 5 Point (5 Point] b. the probability of B tl Point] c. the probability of A and B [I Point] d. the probability of A or B 5 Point) e. the probability of C Assume that the event B has already occurred, find the probability of A. ie P[4B] f. [1 Point]

Explanation / Answer

a) P(A) = P(E1) + P(E2) = 0.22 + 0.31 = 0.53

b) P(B) = P(E2) + P(E3) + P(E4) = 0.31 + 0.15 + 0.22 = 0.68

c) P(A and B) = P(E2) = 0.31

d) P(A or B) = P(A) + P(B) - P(A and B) = 0.53 + 0.68 - 0.31 = 0.9

e) P(Cc) = 1 - P(C) = 1 - (P(E1) + P(E5)) = 1 - (0.22 + 0.1) = 0.68

d) P(A | B) = P(A and B) / P(B) = 0.31 / 0.68 = 0.4589

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