An experiment has three possible outcomes: A, B, and C. If P(A)= P(B)and P(C)= 2P(A), what is the probability of each?

Question

Can anyone help me get started?

Answer 1

Consider that P(A) + P(B) + P(C) = 1.

Answer 2

What do you mean?

Answer 3

The sum of the probabilities of each outcome must equal 1. Therefore, you can find the probability of any outcome by algebra.

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

I'll start you off.

Let x = P(A).

"P(A)= P(B)and P(C)= 2P(A)"

Then x = P(B) and 2x = P(C).

x + x + 2x = 1

Answer 4

So say I got x=1/4 would I substitute it in for P(A through C)?

Answer 5

Yes. x = 1/4, so P(A) = x = 1/4. Similarly, you can find P(B) and P(C).

Answer 6

Alright I think I got it

P(A)= 1/4
P(B)= 2/5
P(C)= 5/14

RIght?

Answer 7

Really good work.

Answer 8

"P(A)= P(B)and P(C)= 2P(A)"

We found that P(A) = x = 1/4. Therefore, P(B) = P(A) = x = 1/4.

P(C) = 2P(A) = 2x = 1/2

You can see that P(A) + P(B) + P(C) = 1/4 + 1/4 + 1/2 = 1