Final answer:
The conditional probability that a customer ordered vanilla ice cream given that they ordered chocolate ice cream is 0.75, or 75%.
Step-by-step explanation:
Peter observed what customers ordered in his ice cream shop and discovered certain probabilities for the ice cream flavors ordered. The probability of a customer ordering vanilla ice cream is denoted as P(vanilla) = 0.3, for chocolate ice cream it's P(chocolate) = 0.2, and the probability of a customer ordering both vanilla and chocolate ice cream is P(vanilla and chocolate) = 0.15. The question requires us to find the conditional probability that a customer ordered vanilla ice cream given that they ordered chocolate ice cream.
To find the conditional probability Q(vanilla | chocolate), we use the formula for conditional probability:
Q(A | B) = P(A and B) / P(B)
In this case, A is the event of ordering vanilla ice cream, and B is the event of ordering chocolate ice cream.
So, Q(vanilla | chocolate) = P(vanilla and chocolate) / P(chocolate)
Let's plug in the values that we have:
Q(vanilla | chocolate) = 0.15 / 0.2
Q(vanilla | chocolate) = 0.75
Therefore, the probability that a customer ordered vanilla ice cream given that they have ordered chocolate ice cream is 0.75 or 75%.