Asked by Rmz

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?

Can anyone help me get started?
Answered by Marth
Consider that P(A) + P(B) + P(C) = 1.
Answered by Rmz
What do you mean?
Answered by Marth
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

Answered by Rmz
So say I got x=1/4 would I substitute it in for P(A through C)?
Answered by Marth
Yes. x = 1/4, so P(A) = x = 1/4. Similarly, you can find P(B) and P(C).
Answered by Rmz
Alright I think I got it

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

RIght?
Answered by bobpursley
Really good work.
Answered by Marth
"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