Question

Suppose that a sample space has five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E2} B = {E3, E4} C = {E2, E3, E5} Find P(A), P(B), and P(C).

Answer 1

The probabilities for events A, B, and C are 40%, 40%, and 60%, respectively, given a sample space with five equally likely outcomes.

Step-by-step explanation:

Let's calculate the probabilities for events A, B, and C given a sample space of five equally likely outcomes E1, E2, E3, E4, and E5. To do so, we count the number of favorable outcomes for each event and divide by the total number of outcomes in the sample space.

• Event A = {E1, E2} has 2 favorable outcomes.
• Event B = {E3, E4} also has 2 favorable outcomes.
• Event C = {E2, E3, E5} has 3 favorable outcomes.

Since each outcome is equally likely, the probabilities are calculated as:

• P(A) = Number of favorable outcomes for A / Total number of outcomes in the sample space = 2/5.
• P(B) = Number of favorable outcomes for B / Total number of outcomes in the sample space = 2/5.
• P(C) = Number of favorable outcomes for C / Total number of outcomes in the sample space = 3/5.

Thus, the probabilities are:

• P(A) = 2/5 or 40%
• P(B) = 2/5 or 40%
• P(C) = 3/5 or 60%