Question

question 1 of 5 select the correct answer. of the 19 houses on jays street, 7 have a black mailbox, 6 have a stone driveway, and 4 have both a black mailbox and a stone driveway. what is the probability that a randomly selected house on jays street has a black mailbox or a stone driveway? $\frac{5}{19}$ $\frac{13}{19}$ $\frac{17}{19}$ $\frac{9}{19}$

Explanation:

Step1: Recall probability formula

The formula for the probability of the union of two events $A$ and $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that a house has a black mailbox and $B$ be the event that a house has a stone driveway. We know that $n = 19$ (total number of houses), $n(A)=7$, $n(B)=6$ and $n(A\cap B)=4$.

Step2: Calculate individual and intersection probabilities

$P(A)=\frac{n(A)}{n}=\frac{7}{19}$, $P(B)=\frac{n(B)}{n}=\frac{6}{19}$ and $P(A\cap B)=\frac{n(A\cap B)}{n}=\frac{4}{19}$.

Step3: Calculate the probability of the union

$P(A\cup B)=\frac{7}{19}+\frac{6}{19}-\frac{4}{19}=\frac{7 + 6-4}{19}=\frac{9}{19}$.

Answer:

$\frac{9}{19}$