Question

Suppose that among all U.S. Students, 80% have gone to an amusement park and 45% have gone to a beach. Only 15% have done neither. If you select a student at random, what is the probability that the student has gone to the beach but not to an amusement park

Answer 1

5%

Explanation:

Let x represent the percentage of people that have gone to both the park and the beach.

The percentage of people that have gone only to the amusement park = 80% - x% = 80 - x

The percentage of people that have gone only to the beach = 45% - x% = 45 - x

Therefore:

100% = (80 - x) + (45 - x) + (x) + (15)

100 = 80 + 45 + 15 -x - x + x

100 = 140 - x

x = 140 - 100

x = 40%

Therefore 40% of the students have gone to both the park and the beach.

The probability that the student has gone to the beach but not to an amusement park = 45% - 40% = 5%