Question

a lawn mowing service company surveyed randomly selected families in a community about mowing their lawn. the results are shown in the table. determine the indicated probabilities. round your answer to the nearest whole percent. type the correct answer in each box. for help, see this worked example g. p(pays for lawn service|has children) = % p(has no children|mows own lawn) = %

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. For $P(\text{has no children}|\text{mows own lawn})$, $A$ is the event of having no children and $B$ is the event of mowing one's own lawn. The number of people who mow their own lawn is $91$ (the total in the "Mows Own Lawn" row), and the number of people who mow their own lawn and have no children is $54$. So $P(\text{has no children}|\text{mows own lawn})=\frac{54}{91}\approx 0.5934$. As a percentage, it is $0.5934\times100 = 59.34\%\approx59\%$.

Step2: Recall conditional - probability formula for the second case

For $P(\text{pays for lawn service}|\text{has children})$, $A$ is the event of paying for lawn service and $B$ is the event of having children. The number of people who have children is $120$ (the total in the "Has Children" column), and the number of people who have children and pay for lawn service is $83$. So $P(\text{pays for lawn service}|\text{has children})=\frac{83}{120}\approx 0.6917$. As a percentage, it is $0.6917\times 100=69.17\%\approx69\%$.

Answer:

$P(\text{has no children}|\text{mows own lawn}) = 59\%$
$P(\text{pays for lawn service}|\text{has children}) = 69\%$