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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?

A. [tex]P(\text{late departure or early arrival}) = 0.12 + 0.04[/tex]

B. [tex]P(\text{late departure or early arrival}) = 0.12 + 0.27[/tex]

C. [tex]P(\text{late departure or early arrival}) = 0.12 + 0.27 - 0.04[/tex]

D. [tex]P(\text{late departure or early arrival}) = 0.27 + 0.04 - 0.12[/tex]

Sagot :

GinnyAnsweridn
To determine the probability of either a late departure or an early arrival, we need to use the principle of calculating the probability of the union of two events in probability theory. The formula we use is:

[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]

Where [tex]\( P(A) \)[/tex] represents the probability of event A occurring (in this case, a late departure), [tex]\( P(B) \)[/tex] represents the probability of event B occurring (an early arrival), and [tex]\( P(A \text{ and } B) \)[/tex] represents the probability of both events occurring simultaneously (both a late departure and an early arrival).

Given the probabilities:
- Probability of a late departure ([tex]\( P(A) \)[/tex]): 0.12
- Probability of an early arrival ([tex]\( P(B) \)[/tex]): 0.27
- Probability of both a late departure and an early arrival ([tex]\( P(A \text{ and } B) \)[/tex]): 0.04

Using the formula, we can substitute these values in:

[tex]\[ P(\text{late departure or early arrival}) = 0.12 + 0.27 - 0.04 \][/tex]

So the correct equation to calculate the probability of a late departure or an early arrival is:

[tex]\[ P(\text{late departure or early arrival}) = 0.12 + 0.27 - 0.04 \][/tex]

Therefore, the correct answer is:

[tex]\[ P(\text{late departure or early arrival}) = 0.12 + 0.27 - 0.04 \][/tex]
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