Question

A sample space of an experiment is {A, B, C}. Find the probability of each simple outcome if P (A) = P (B) and P (C) = 2P (A).

Answer 1

To find the probability of each simple outcome, we can assign a value to P(A) based on the given information. Then we can use this value to find P(B) and P(C).

Step-by-step explanation:

To find the probability of each simple outcome, we need to assign a value to P(A) and P(C) based on the given information. Let's assume that P(A) = x, then P(B) = x as well. And since P(C) = 2P(A), we can say that P(C) = 2x.

Since the sample space is {A, B, C}, the total probability is equal to 1, so we have the equation x + x + 2x = 1. Simplifying, we get 4x = 1, which means x = 1/4.

Now we can find the probability of each simple outcome: P(A) = P(B) = 1/4, and P(C) = 2(1/4) = 1/2.