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?
Hint: We know that in this case, P(A)+ P(B)+P(C)=1; therefore,P(A)+P(A)+2P(A)=1
Please Help :)
So 4P(A)=1,or
P(A)=1/4=0.25
Can you take it from here?
To find the probability of each event, we can use the information given:
Let's assume the probability of event A is P(A).
Since P(A) = P(B), the probability of event B will also be P(A).
Now, P(C) = 2P(A).
We can rewrite the equation as:
P(A) + P(A) + 2P(A) = 1
Combine like terms:
4P(A) = 1
To find the value of P(A), divide both sides of the equation by 4:
P(A) = 1/4
Now let's find the probability of events A, B, and C:
P(A) = 1/4
P(B) = P(A) = 1/4
P(C) = 2P(A) = 2 * (1/4) = 2/4 = 1/2
So, the probabilities of events A, B, and C are:
P(A) = 1/4
P(B) = 1/4
P(C) = 1/2