Suppose that an experiment has four possible outcomes: A, B, C, and D. If P(A) = P(B) = P(C) and what is the probability of each event?

The probability of D is

P(D) = 1 - 3 P(A)

You have already stated the other probabilities. Specific numerical values depend upon what P(A) is. There is a range of possibilites from 0 to 1/3.

To determine the probability of each event, we need to consider that the sum of the probabilities of all possible outcomes must equal 1. Since we have four outcomes, let's denote the probability of each event as P(A), P(B), P(C), and P(D).

Given that P(A) = P(B) = P(C), let's say that the probability of each event is x. Therefore, we have:

P(A) = x
P(B) = x
P(C) = x

Since the sum of the probabilities of all possible outcomes must equal 1, we can write:

P(A) + P(B) + P(C) + P(D) = 1

Substituting the values of P(A), P(B), and P(C), we get:

x + x + x + P(D) = 1

3x + P(D) = 1

Since P(D) represents the probability of event D, we can say that P(D) = 1 - 3x.

To find the value of x, we can use the fact that P(A) = P(B) = P(C). Therefore:

P(A) + P(B) + P(C) = 3x

Substituting x for probability values, we get:

x + x + x = 3x

3x = 1

Dividing by 3 on both sides, we find:

x = 1/3

Now, we can substitute the value of x back into P(D):

P(D) = 1 - 3x = 1 - 3(1/3) = 1 - 1 = 0

So, the probability of events A, B, and C is 1/3 each, while the probability of event D is 0.