P(E)=.4, P(F)=.5 and P(E[intersect]F)=.1 , Calculate P(F[suchthat]E)=?
Using conditional probability, I got .2 as the answer, right?
Is the answer the same for P(EsuchthatF)?
wouldn't it be .25? check my thinking.
Bob Pursley - Thank-you! I figured out how you got .25
To calculate P(F|E) (the probability of event F given that event E has occurred), we can use the formula:
P(F|E) = P(E ∩ F) / P(E)
Given that P(E) = 0.4, P(F) = 0.5, and P(E ∩ F) = 0.1, we can substitute these values into the formula:
P(F|E) = 0.1 / 0.4
Simplifying this expression, we get:
P(F|E) = 0.25
So, the probability of event F given that event E has occurred is 0.25.
Now, let's calculate P(E|F) (the probability of event E given that event F has occurred). To do this, we can use the same formula as before:
P(E|F) = P(E ∩ F) / P(F)
We know that P(F) = 0.5 and P(E ∩ F) = 0.1, so we can substitute these values into the formula:
P(E|F) = 0.1 / 0.5
Simplifying this expression, we get:
P(E|F) = 0.2
Therefore, the probability of event E given that event F has occurred is 0.2.
So, the answer is different for P(E|F), which is 0.2, compared to P(F|E), which is 0.25.