An experiment consists of 8 possible outcomes labelled, say, as a1; a2; : : : ;

Question

An experiment consists of 8 possible outcomes labelled, say, as a1; a2; : : : ; a8. Each outcome has an equal probability of occurring. Define the following events from the sample space of this experiment: A = {a1, a2, a3, a4} B = {a1, a2, a6, a7} and C = {a1, a3, a5, a8} (a) (3 points) Calculate P(A and B) and compare this with P(A) x P(B). (b) (3 points) Calculate P(A and C) and compare this with P(A)  x P(C). (c) (3 points) Calculate P(B and C) and compare this with P(B) x  P(C). (d) (3 points) Calculate P(A and B and C) and compare this with P(A) x  P(B) x P(C).

Explanation / Answer

a)P(A and B) = 2/8=1/4 (a1, a2) P(A) X P(B) = 4/8 * 4/8 = 1/4 b)P(A and C) = 2/8=1/4 (a1, a3) P(A) X P(C) = 4/8 * 4/8 = 1/4 c)P(B and C) = 1/8 (a1) P(B) X P(C) = 4/8 * 4/8 = 1/4 b)P(A and B and C) = 1/8 (a1) P(A) X P(B) X P(C) = 4/8 * 4/8 * 4/8= 1/8

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