Question

an airline gathers data on late departures and early arrivals over a month. it finds that the probability of a late departure is 12 percent, the probability of an early arrival is 27 percent, and the probability of both a late departure and an early arrival is 4 percent. which equation shows how to correctly calculate the probability of a late departure or an early arrival?
p(late departure or early arrival) = 0.12 + 0.04
p(late departure or early arrival) = 0.12 + 0.27
p(late departure or early arrival) = 0.12 + 0.27 - 0.04
p(late departure or early arrival) = 0.27 + 0.04 - 0.12

Explanation:

Step1: Recall the addition - rule of probability

For two events $A$ and $B$, the probability of $A$ or $B$ is given by $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event of a late - departure and $B$ be the event of an early - arrival.

Step2: Identify the given probabilities

We are given that $P(A) = 0.12$ (probability of a late departure), $P(B)=0.27$ (probability of an early arrival), and $P(A\cap B)=0.04$ (probability of both a late departure and an early arrival).

Step3: Apply the addition - rule formula

Substitute the values into the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. So $P(\text{late departure or early arrival})=0.12 + 0.27-0.04$.

Answer:

$P(\text{late departure or early arrival}) = 0.12 + 0.27-0.04$ (the third option)