If the probability that Jenna will go for coffee given that she has gone to the movies is 5/7, and the probability that she will go to both the movies and for coffee is 1/4, we can use conditional probability to find the probability that Jenna will go to the movies on any particular Saturday.
Let's use the formula for conditional probability:
P(A|B) = P(A and B)/P(B)
In this case, A represents going to the movies and B represents going for coffee.
We know that P(A and B) = 1/4 and P(B) = 5/7.
Plugging these values into the formula:
P(A|B) = (1/4)/(5/7)
To simplify this expression, we can multiply the numerator and denominator by the reciprocal of 5/7, which is 7/5:
P(A|B) = (1/4) * (7/5) = 7/20
Therefore, the probability that Jenna will go to the movies on any particular Saturday is 7/20.