# Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, . . . , E7 denote the sample points. The following probability assignments apply: P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05. Let A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7} Find the probability of the intersection of A and B.

1 answer

###### Question:

Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, . . . , E7 denote the sample points. The following probability assignments apply:

P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05.

Let A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7}

Find the probability of the intersection of A and B.

P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05.

Let A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7}

Find the probability of the intersection of A and B.

## Answers

Answer:The required probability for the intersection of A & B = 0.25Step-by-step explanation:Given that:Sample space S = {E1, E2, E3, E4, E5, E6, E7} and the probability of each sample points are:P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05.Also;A = {E1, E4, E6}B = {E2, E4, E7} C = {E2, E3, E5, E7}Then P(A) = 0.05 + 0.25 + 0.10 = 0.4P(B) = 0.20 + 0.25 + 0.05 = 0.5P(C) = 0.20 + 0.20 + 0.15 + 0.05 = 0.6The intersection of A and B are:P(A ∩ B) = E4P(A ∩ B) = 0.25The required probability for the intersection of A & B = 0.25

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