Question

(1 pt) Real estate ads suggest that 57 % of homes for sale have garages. 29 % have swimming pools, and 25 % 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

A :- Have Swimming pool

B :- Have Garage

P ( A ) = 0.29

P ( B ) = 0.57

$P ( A\cap B) = 0.25$

Part a)

P ( A or B ) = P ( A ) + P ( B ) - $P ( A\cap B)$

P ( A or B ) = 0.29 + 0.57 - 0.25 = 0.61

P ( A or B ) = 0.61

Part b)

P ( nor A and nor B ) = 1 - P ( A and B )

P ( nor A and nor B ) = 1 - 0.25

P ( nor A and nor B ) = 0.75

Part c)

P ( A and not B ) = P ( A ) - P ( A and B )

P ( A and not B ) = 0.29 - 0.25

P ( A and not B ) = 0.04