Question

Real estate ads suggest that 58% of homes for sale have garages, 41% have swimming pools, and 38% have both features. What is the probability that a home for sale: (a) has a pool or a garage? (b) neither a pool nor a garage? (c) a pool but no garage?

Answer 1

The probability of a home for sale having either a pool or a garage is 61%. The probability of a home for sale having neither a pool nor a garage is 39%. The probability of a home for sale having a pool but no garage is 3%.

Step-by-step explanation:

The question involves probability and the use of the inclusion-exclusion principle for calculating probabilities.

Part a: Probability of a home for sale having a pool or a garage

The probability can be calculated using the formula P(A or B) = P(A) + P(B) - P(A and B).

P(garage or pool) = P(garage) + P(pool) - P(garage and pool)
= 0.58 + 0.41 - 0.38
= 0.61 or 61%

Part b: Probability of a home for sale having neither a pool nor a garage

We can calculate this by subtracting the probability of a home having either feature from 1.
1 - P(garage or pool) = 1 - 0.61 = 0.39 or 39%

Part c: Probability of a home for sale having a pool but no garage

This is found by subtracting the probability of a home having both features from the probability of a home having a pool.
P(pool but no garage) = P(pool) - P(garage and pool)
= 0.41 - 0.38
= 0.03 or 3%