If E and F are events with P ( E ∩ F ) = 0.09 and P ( E F ) = 0.3 , P ( F E ) = 0.4
Find P (F )
I assume the question was:
If E and F are events with P ( E ∩ F ) = 0.09 and P ( E | F ) = 0.3 , P ( F | E ) = 0.4
Find P (F )
where P(E|F) and P(F|E) are conditional probabilities.
Review your class notes to find that:
P(E|F)=P(E∩F)/P(F)
and
P(F|E)=P(F∩E)/P(E)=P(E∩F)/P(E)
From the above equations, you can solve for P(F) and P(E) respectively.
To find P(F), we need to use the formula for the probability of the union of two events: P(E ∪ F) = P(E) + P(F) - P(E ∩ F)
Given that P(E ∩ F) = 0.09 and P(E ∩ F) = 0.3, we can substitute these values into the formula:
P(E ∪ F) = P(E) + P(F) - P(E ∩ F)
P(E ∪ F) = 0.3 + P(F) - 0.09
Now, we need to find P(E ∪ F). This is the probability of the union of events E and F, which can also be written as the probability of either event E occurring, event F occurring, or both occurring.
However, we don't have any information about the individual probabilities of events E or F. Therefore, without further information, it's not possible to find the exact value of P(F).
If you have additional information about the individual probabilities of events E or F, or any other relevant information, please provide it so that we can calculate the value of P(F).