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?