# Question

An experiment results in one of five sample points with the following probabilities: P(E1) = .22, P(E2) = .31,P(E3) = .15, P(E4) = .22, and P(E5) = .1. The following events have been defined:

A: {E1, E3}

B: {E2, E3, E4}

C: {E1, E5}

Find each of the following probabilities:

a. P (A)

b. P (B)

c. P(A ∩ B)

d. P(A | B)

e. P(B ∩ C)

f. P(C | B)

g. Consider each pair of events A and B, A and C, and B and C. Are any of the pairs of events independent? Why?

A: {E1, E3}

B: {E2, E3, E4}

C: {E1, E5}

Find each of the following probabilities:

a. P (A)

b. P (B)

c. P(A ∩ B)

d. P(A | B)

e. P(B ∩ C)

f. P(C | B)

g. Consider each pair of events A and B, A and C, and B and C. Are any of the pairs of events independent? Why?

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