Question

homework 34: problem 6 (1 point) results for this submission 1 of the answers is not correct. 1 of the questions remains unanswered. real estate ads suggest that 60% of homes for sale have garages, 21% have swimming pools, and 19% have both features. what percentage of homes for sale have a) a pool or a garage? answer = 62 % b) neither a pool nor a garage? answer = 1 % c) a pool but no garage? answer = % note: enter your answers as percentages, not decimals. note: you can earn partial credit on this problem.

Explanation:

Step1: Recall the formula for the union of two events

Let $A$ be the event that a home has a garage and $B$ be the event that a home has a pool. We know that $P(A)=0.6$, $P(B) = 0.21$, and $P(A\cap B)=0.19$. The formula for $P(A\cup B)$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

Step2: Calculate the percentage of homes with a pool or a garage

$P(A\cup B)=0.6 + 0.21- 0.19=0.62$ or $62\%$.

Step3: Calculate the percentage of homes with neither a pool nor a garage

The total percentage of all homes is $100\%$ or $1$. The percentage of homes with a pool or a garage is $P(A\cup B) = 0.62$. So the percentage of homes with neither a pool nor a garage is $1 - P(A\cup B)=1 - 0.62 = 0.38$ or $38\%$.

Step4: Calculate the percentage of homes with a pool but no garage

The percentage of homes with a pool but no garage is $P(B)-P(A\cap B)$. So $0.21 - 0.19=0.02$ or $2\%$.

Answer:

b) $38\%$
c) $2\%$