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(\text{late departure or early arrival}) = 0.12 + 0.04\\)
\\(p(\text{late departure or early arrival}) = 0.12 + 0.27\\)
\\(p(\text{late departure or early arrival}) = 0.12 + 0.27 - 0.04\\)
\\(p(\text{late departure or early arrival}) = 0.27 + 0.04 - 0.12\\)

Explanation:

Identify the given probabilities

Using the Theoretical Probability knowledge point

$$
LATEXBLOCK0
$$

Apply the Addition Rule for Probability

To find the probability of a late departure or an early arrival, we use the general addition rule for any two events \(A\) and \(B\):

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

Substituting our values:

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

Answer:

• \(P(\text{late departure or early arrival}) = 0.12 + 0.04\)
• \(P(\text{late departure or early arrival}) = 0.12 + 0.27\)
• \(P(\text{late departure or early arrival}) = 0.12 + 0.27 - 0.04\) (Correct answer)
• \(P(\text{late departure or early arrival}) = 0.27 + 0.04 - 0.12\)