Question

Among middle school students, 65% like chocolate ice cream, 50% like vanilla ice cream, and 30%like both. Suppose a student is selected at random and asked what type(s) of ice cream they like. Determine the probability that a randomly selected middle school student likes chocolate ice cream, butnot vanilla ice cream.

Answer 1

The probability that a randomly selected middle school student likes chocolate ice cream but not vanilla ice cream is 35%.

How to determine the probability

To determine the probability that a randomly selected middle school student likes chocolate ice cream but not vanilla ice cream, subtract the probability of liking both chocolate and vanilla ice cream from the probability of liking chocolate ice cream.

Given the following information:

65% of middle school students like chocolate ice cream.

50% of middle school students like vanilla ice cream.

30% of middle school students like both chocolate and vanilla ice cream.

Let's denote the probability of liking chocolate ice cream as P(chocolate) and the probability of liking vanilla ice cream as P(vanilla).

P(chocolate) = 65%

P(vanilla) = 50%

P(both) = 30%

To find the probability of liking chocolate but not vanilla, we can use the formula:

P(chocolate but not vanilla) = P(chocolate) - P(both)

P(chocolate but not vanilla) = 65% - 30%

P(chocolate but not vanilla) = 35%

Therefore, the probability that a randomly selected middle school student likes chocolate ice cream but not vanilla ice cream is 35%.

Answer 2

Since there are 65% like chocolate ice cream

Since 30% like both chocolate and vanilla

Then to find who like chocolate only subtract 30% from 65%

Then P(choco. only = 65% - 30% = 35%

Then the probability that a student is chosen randomly likes chocolate but not vanilla is 35%

The answer is 35%