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) = 0.05, P(E2) = 0.15, P(E3) = 0.1, P(E4) = 0.25, P(E5) = 0.1, P(E6) = 0.1, and P(E7) = 0.25. Assume the following events when answering the questions. A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7} Find P(A), P(B), and P(C).

Answer 1

To find the probability of events A, B, and C, we sum the probabilities of their respective sample points.

Step-by-step explanation:

To find the probability of an event, we sum the probabilities of its sample points.

For event A, which consists of the sample points E1, E4, and E6, the probability is:

P(A) = P(E1) + P(E4) + P(E6) = 0.05 + 0.25 + 0.1 = 0.4

Similarly, for event B and event C, we have:

P(B) = P(E2) + P(E4) + P(E7) = 0.15 + 0.25 + 0.25 = 0.65

P(C) = P(E2) + P(E3) + P(E5) + P(E7) = 0.15 + 0.1 + 0.1 + 0.25 = 0.6