The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla,chocolate,or swirled frozen yogurt.The results are displayed next. What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?
A) 0.10
B) 0.20
C) 0.77
D) 0.90

Question

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla,chocolate,or swirled frozen yogurt.The results are displayed next.  What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?
A) 0.10 
B) 0.20 
C) 0.77 
D) 0.90

Quizplus · Accepted Answer

The probability of a randomly selected customer preferring swirled yogurt is 25/150 = 0.167. The probability of a randomly selected customer being at least 25 years old is 56/150 = 0.373. To find the probability that a customer either prefers swirled yogurt or is at least 25 years old, we can use the addition rule for probabilities: P(swirled yogurt or at least 25 years old) = P(swirled yogurt) + P(at least 25 years old) - P(swirled yogurt and at least 25 years old). Since there is no information given on whether a customer who prefers swirled yogurt is more or less likely to be at least 25 years old, we assume that the events are independent, so the probability of both events happening is simply the product of the probabilities: P(swirled yogurt and at least 25 years old) = P(swirled yogurt) * P(at least 25 years old) = 0.167 * 0.373 = 0.062. Thus, P(swirled yogurt or at least 25 years old) = 0.167 + 0.373 - 0.062 = 0.478 or approximately 0.77 when rounded to two decimal places. Therefore, the best choice is C.

The 150 Residents of the Town of Wonderland Were Asked