Real estate ads suggest that 58 % of homes for sale have garages, 39 % have swimming pools, and 6 % have both features. What is the probability that a home for sale has a) a pool or a garage? b) neither a pool nor a garage? c) a pool but no garage?

Answer: (a) 0.91

(b) 0.09

(c) 0.33

Step-by-step explanation:

Let probability of having a garage be P (G) = 0.58

And probability of having a swimming pool P (p) = 0.39

Probability of having both P (G and p) = 0.06

(a) P (pool or garage) = P (p) + P (G) - P (P and G)

Using the general addition rule add the probability of a house with a pool plus the probability of a house with a garage and subtract the probability of a house with both a garage and a pool.

= 0.58 + 0.39 - 0.06

= 0.91

(b) P (neither pool nor garage) = 1 - P (pool or garage)

Probability of not having a pool nor a garage can be found by subtracting the probability of having a pool or a garage.

= 1 - 0.91

= 0.09

(c) P (pool and no garage) = P (p) - P (p and G)

Probability of a house with a pool but no garage can be found by subtracting the probability of having both a pool and a garage from the one of having only a pool.

= 0.39 - 0.06

= 0.33