A refreshment stand sells popcorn and soft drinks. Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. 38 students bought both popcorn and a drink.
What is the probability that a student buys a drink, given that he or she buys popcorn?
To find the probability that a student buys a drink given that he or she buys popcorn, we need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
Where P(A|B) is the probability of event A occurring given that event B has occurred, P(B) is the probability of event B occurring, and P(A and B) is the probability of both event A and event B occurring.
In this case, event A is buying a drink, event B is buying popcorn.
P(A and B) is the number of students who bought both popcorn and a drink, which is 38.
P(B) is the number of students who bought popcorn, which is 62.
Therefore, the probability that a student buys a drink given that he or she buys popcorn is:
P(A|B) = 38 / 62 ≈ 0.613.
So, the probability is approximately 0.613 or 61.3%.