Questions: 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) 0.21 (B) 0.23 (C) 0.26 (D) 0.39 (E) 0.72

Solution Steps

To find the probability of a flight being late, we use the total probability of flights arriving early and on time: \[ P(L) = 1 - (P(E) + P(O)) = 1 - (0.15 + 0.25) = 1 - 0.40 = 0.60 \]

We know the probability of flights being late or not overbooked. To find the probability of a flight being late and not overbooked, we can use the following relationship: \[ P(L \cap \neg B) = P(L \cup \neg B) - P(\neg B) \] Where \( P(\neg B) = 1 - P(B) = 1 - 0.65 = 0.35 \). Thus, \[ P(L \cap \neg B) = 0.72 - 0.35 = 0.37 \]

Final Answer