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Question 8, 8.6.23-BE
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In 2020, the total number of motor vehicles produced in the world was 76 million. The probability that a vehicle was produced in Country A was 0.35 . The probability that a vehicle was produced in Country B was 0.13 . The probability that a vehicle was produced in another country (call it Country C) was 0.52 . The probability that a vehicle produced in Country A was a passenger car was 0.48 . The probability that a vehicle produced in Country B was a passenger car was 0.24 . The probability that a vehicle produced in Country $\mathrm{C}$ was a passenger car was 0.69 . Given that the vehicle sold was not a passenger car, find the probability it was made in neither Country A nor Country B.

Given that the vehicle sold was not a passenger car, the probability it was made in neither Country A nor Country B is $\square$.
(Do not round until the final answer. Then round to four decimal places as needed.)
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$11 / 13 / 2023$

Step 1 ：Define the events: Event A is that the vehicle was made in neither Country A nor Country B and event B is that the vehicle was not a passenger car.

Step 2 ：Calculate the probability of event A, P(A), which is the probability that a vehicle was made in Country C, 0.52.

Step 3 ：Calculate the probability of event B, P(B), which is the probability that a vehicle was not a passenger car. This can be found by subtracting the probabilities that a vehicle was a passenger car in each country from 1. The probabilities are 0.48 for Country A, 0.24 for Country B, and 0.69 for Country C. So, P(B) = 1 - (0.48*0.35 + 0.24*0.13 + 0.69*0.52) = 0.442.

Step 4 ：Calculate the probability of both events A and B occurring, P(A ∩ B), which is the probability that a vehicle was made in Country C and was not a passenger car. This can be found by multiplying the probability that a vehicle was made in Country C by the probability that a vehicle made in Country C was not a passenger car. So, P(A ∩ B) = 0.52 * (1 - 0.69) = 0.1612.

Step 5 ：Substitute these probabilities into the formula for conditional probability to find the answer. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B). So, P(A|B) = 0.1612 / 0.442 = 0.3647.

Step 6 ：Final Answer: The probability that a vehicle was made in neither Country A nor Country B given that it was not a passenger car is \( \boxed{0.3647} \).