suppose that an experiment has four possible outcomes. a,b,c and d. if p(a)= p(b)= p(c) and p(d)= 2p(a) what is the probabilty of each event

If p(a)= p(b)= p(c) and p(d)= 2p(a), then

5p(a) = 1.

You should be able to take it from there.

To calculate the probability of each event, we need to consider that the sum of all probabilities must be equal to 1. Let's denote the probability of event A as p(A), the probability of event B as p(B), the probability of event C as p(C), and the probability of event D as p(D).

Given the information provided:
p(A) = p(B) = p(C)
p(D) = 2p(A)

To find the probability for each event, we can set up equations based on the given information:

Equation 1: p(A) + p(B) + p(C) + p(D) = 1 (because the sum of all probabilities must be equal to 1)

Equation 2: p(D) = 2p(A) (because p(D) is twice the probability of p(A))

To solve these equations, we can use the fact that p(A) = p(B) = p(C) and that p(D) = 2p(A).

Substituting p(A) for p(B) and p(C) in Equation 1, we have:
p(A) + p(A) + p(A) + 2p(A) = 1

Combining like terms, we get:
5p(A) = 1

Dividing both sides by 5, we find:
p(A) = 1/5

Since p(A) = p(B) = p(C), each of these events has a probability of 1/5 (or 0.2, or 20%).

Additionally, we can find p(D) using Equation 2:
p(D) = 2p(A) = 2(1/5) = 2/5

So, event D has a probability of 2/5 (or 0.4, or 40%).