To solve this problem, we can use the formula for probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
A. To find the probability that a student likes vanilla or chocolate ice cream, but not both, we need to subtract the number of students who like both from the total number of students who like vanilla or chocolate:
Number of students who like vanilla or chocolate = 258 + 142 = 400
Number of students who like both = 102
Number of students who like only vanilla or only chocolate = 400 - 102 = 298
Probability = 298/300 = 0.9933
B. To find the probability that a student likes neither vanilla nor chocolate ice cream, we need to subtract the total number of students who like either or both flavors from the total number of students:
Total number of students = 300
Number of students who like vanilla or chocolate = 258 + 142 = 400
Number of students who like both = 102
Number of students who like neither flavor = 300 - 400 + 102 = 2
Probability = 2/300 = 0.0067
C. To find the probability that a student likes vanilla ice cream but not chocolate ice cream, we need to subtract the number of students who like both from the total number of students who like vanilla:
Number of students who like vanilla = 142
Number of students who like both = 102
Number of students who like only vanilla = 142 - 102 = 40
Probability = 40/300 = 0.1333