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 event
P(A) + P(B) + P(C) = 1 = 5P(A)
P(A) = P(B) = 1/5
P(C) = 2/5
I don't know how drwls got 5P(A).
P(A) + P(B) + P(C) = 1
P(A) + P(A) + 2P(A) = 1 = 4P(A)
P(A) = 1/4 = P(B)
P(C) = 2P(A) = 1/2
Yes, my mistake.
To find the probability of each event, we can assign variables to the probabilities and use the given information to create an equation.
Let's assume that P(A) = x. Since P(A) = P(B), we can say that P(B) = x as well.
According to the given information, P(C) = 2 * P(A). So, P(C) = 2 * x.
Now, we know that the sum of the probabilities of all possible outcomes must be 1. Therefore, we can write the equation as:
P(A) + P(B) + P(C) = 1
Substituting the variables we assigned:
x + x + 2x = 1
Simplifying:
4x = 1
Now, solve for x by dividing both sides of the equation by 4:
x = 1/4
So, the probability of event A (P(A)) and event B (P(B)) is 1/4, and the probability of event C (P(C)) is 2/4 or 1/2.