While investigating customer complaints, the customer relations department of Sonic Air found that 15 percent of the flights arrive early and 25 percent arrive on time. Additionally, 65 percent of the flights are overbooked, and 72 percent are late or not overbooked. One Sonic Air flight will be selected at random. What is the probability that the flight selected will be late and not overbooked? A) 0.2B) 0.26C) 0.72D) 0.23E) 0.38

Question

Mathematics

Natasha

16 April, 21:08

While investigating customer complaints, the customer relations department of Sonic Air found that 15 percent of the flights arrive early and 25 percent arrive on time. Additionally, 65 percent of the flights are overbooked, and 72 percent are late or not overbooked. One Sonic Air flight will be selected at random. What is the probability that the flight selected will be late and not overbooked? A) 0.2B) 0.26C) 0.72D) 0.23E) 0.38

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Answers (1)

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Justice Hartman · Answer 1

P (L ∩ O) = 0.23

Step-by-step explanation:

We are going to define the probabilistic events how:

E: Flights arrive early P (E) = 0.15

T: Flights arrive on time P (T) = 0.25

O: Flights are overbooked P (O) = 0.65

O: Flights are not overbooked

L: Flights arrive late

How 72 percent are late or not overbooked, then P (O ∪ L) = 0.72

Our question is : What is the probability that the flight selected will be late and not overbooked? It means, what is P (L ∩ O)

This probability may be calculated how:

P (L ∩ O) = P (L) + P (O) - P (O ∪ L)

1 = P (L) + P (E) + P (O)

1 = P (L) + 0.15 + 0.25

P (L) = 0.6

how P (0) = 0.65, then P (O) = 0.35

Thus

P (L ∩ O) = 0.6 + 0.35 - 0.72

P (L ∩ O) = 0.23