Question

(1 point) Real estate ads suggest that 57 % of homes for sale have garages,
26 % have swimming pools, and
24 % have both features.
What is the probability that a home for sale has
a) a pool or a garage?
Answer =  %
b) neither a pool nor a garage?
Answer =  %
c) a pool but no garage?
Answer =  %

Answer 1

Let 'G' be houses having garages and 'S' for swimming pools

P(G) = 57% P(S) = 26% P(Both) = = 24%

a) a pool or a garage?

A pool or a garage means union of pool and garage. So we can use addition probability

= 57% + 26% - 24%
Answer = 59%

b) neither a pool nor a garage?

This means both should not be there. So we have union meaning at least 1, it's complement would be none

neither a pool nor a garage = 1 - a pool or a garage

= 1 - 59%
Answer = 41%

c) a pool but no garage?

Means only pool. So we remove the intersection (both probability) from individual probbaility of pool

= P(S) -

= 26% - 24%
Answer = 2%