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Chapter 4: Problem 93

Suppose that \(20 \%\) of all adults in a small town live alone, and \(8 \%\) of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?

Short Answer

Expert verified
The probability that a randomly selected adult from this town has at least one pet given that this adult lives alone is 40%.

Step by step solution

01

Identify the Given Probabilities

20 \% is the probability of an adult living alone in the small town, this is defined as event B. From the total adults, 8 \% both live alone and have at least one pet, this can be defined as the intersection of two events A and B, \(P(A 鈭� B)\).
02

Applying Conditional Probability Formula

The aim is to find the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone. This is a conditional probability problem. According to the formula for Conditional Probability which is \(P(A|B) = P(A 鈭� B) / P(B)\) where, \(P(A|B)\) is the conditional probability of event A given event B, \(P(A 鈭� B)\) is the probability of both events A and B happening, and \(P(B)\) is the probability of event B.
03

Calculate the Conditional Probability

Plugging in the given values in the formula, we get \(P(A|B) = (8/100) / (20/100) = 0.4\) or 40 \%.

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Most popular questions from this chapter

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