15 Please calculate P(E|F) given P(F|E)=0.3, =0.25 and P(E)=0.6

Many basic math problems can be solved by understanding the definition of terms.

Conditional probability
P(E|F)=conditional probability that event E will occur given that event F has already occurred
= P(E∩F)/P(F)
Therefore
P(F|E)=P(F∩E)/P(E)
=P(E∩F)/P(E)
since the ∩ operator is commutative.
Substitute values and solve for P(E∩F).
Note: You seem to have omitted something that equals 0.25

To calculate P(E|F) given the probabilities P(F|E) = 0.3, P(F) = 0.25, and P(E) = 0.6, you can use Bayes' Theorem. Bayes' Theorem is a way to calculate conditional probabilities by using the reverse conditional probabilities and the probabilities of the individual events.

The formula for Bayes' Theorem is:

P(E|F) = (P(F|E) * P(E)) / P(F)

According to the given information, we have:

P(F|E) = 0.3 (the probability of F given E)
P(E) = 0.6 (the probability of E)
P(F) = 0.25 (the probability of F)

Now, we can substitute these values into the formula to calculate P(E|F):

P(E|F) = (0.3 * 0.6) / 0.25

Calculating this expression gives us:

P(E|F) = 0.18 / 0.25

P(E|F) = 0.72

Therefore, P(E|F) is equal to 0.72, or 72%.