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?
14 years ago
14 years ago
What do you mean?
14 years ago
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
14 years ago
So say I got x=1/4 would I substitute it in for P(A through C)?
14 years ago
Yes. x = 1/4, so P(A) = x = 1/4. Similarly, you can find P(B) and P(C).
14 years ago
Alright I think I got it
P(A)= 1/4
P(B)= 2/5
P(C)= 5/14
RIght?
14 years ago
Really good work.
14 years ago
"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
11 months ago
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