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?

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

What do you mean?

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

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

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

Alright I think I got it

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

RIght?

Really good work.

"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

Of course! To find the probabilities of A, B, and C, we can start by assigning a variable to one of the probabilities and expressing the other probabilities in terms of that variable.

Let's say the probability of A is x. Since P(A) = P(B), the probability of B is also x.

According to the given information, P(C) = 2P(A). Substituting the value of P(A) with x, we can say P(C) = 2x.

Now, to find the overall probability, we sum up the probabilities of all possible outcomes, which should equal 1.

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

Substituting x for P(A) and x for P(B), we have:

x + x + 2x = 1

Simplifying the equation, we get:

4x = 1

To find x, we divide both sides by 4:

x = 1/4

So the probability of A (P(A)) and B (P(B)) is 1/4, and the probability of C (P(C)) is 2 times that:

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

Therefore, the probabilities are:
P(A) = 1/4
P(B) = 1/4
P(C) = 1/2