Final answer:
P = 63/64
The probability that Jeffrey goes to Cafe Shirley for a coffee, given that each of his friends has a 3/4 chance of going, is 63/64 because he will only go if at least one friend is present.
Step-by-step explanation:
To calculate the probability that Jeffrey goes to Cafe Shirley for a coffee, we must first consider the probability that none of his friends go to the cafe.
Since Chris, Nina, and Iana each have a 3/4 chance of going to the cafe, the probability that any one of them doesn't go is 1 - 3/4 = 1/4.
We then calculate the probability that none of them go, which is the product of each person's individual probability of not going: (1/4) * (1/4) * (1/4) = 1/64.
Therefore, the probability that at least one of them does go to the cafe is 1 - 1/64 = 63/64.
Consequently, this is also the probability that Jeffrey goes to Cafe Shirley for a coffee since he only goes if at least one of his friends is there.