Given:
P(E)=0.4
P(F)=0.8
P(F∣E)=0.6
We need to find P(E∣F), which is the probability of E happening given that F has already happened.
To find this, we'll use the conditional probability formula, but first we need to find P(E∩F).
We're given P(F∣E)=0.6. Using the conditional probability formula:
P(F∣E)=P(E)P(E∩F)
Rearranging:
P(E∩F)=P(F∣E)×P(E)
P(E∩F)=0.6×0.4
P(E∩F)=0.24
Now we can find P(E∣F) using:
P(E∣F)=P(F)P(E∩F)
Substituting the values:
P(E∣F)=0.80.24
P(E∣F)=0.3
Therefore, P(E∣F)=0.3