Question

Rac is an automotive dealer selling imported new cars, and a number of them are japanese cars. the manager of rac found that 60% of the customers visited them but didn’t purchase anything. about 25% bought an imported new car and 45% bought a japanese car. what is the probability a customer visited them and bought an imported new japanese car?

Answer 1

To find the probability that a customer visited RAC and bought an imported new Japanese car, we need to find the intersection of the two events: visiting RAC and buying an imported new Japanese car. The probability can be calculated using the formula P(A and B) = P(A) * P(B|A), where P(A) is the probability of event A, and P(B|A) is the probability of event B given that event A has occurred. Given the provided probabilities, the probability of a customer visiting RAC and buying an imported new Japanese car is 11.25%.

Step-by-step explanation:

To find the probability that a customer visited RAC and bought an imported new Japanese car, we need to find the intersection of the two events: visiting RAC and buying an imported new Japanese car. We can use the formula for finding the probability of the intersection of two events: P(A and B) = P(A) * P(B|A), where P(A) is the probability of event A, and P(B|A) is the probability of event B given that event A has occurred.

Given that 60% of customers visited RAC but didn't purchase anything, the probability of visiting RAC without buying is 0.6. The probability of buying an imported new car is 25% and the probability of buying a Japanese car is 45%. So, the probability of buying an imported new Japanese car given that the customer visited RAC is: P(imported new Japanese | visited RAC) = P(imported new | visited RAC) * P(Japanese | visited RAC) = 0.25 * 0.45 = 0.1125 or 11.25%

Answer 2

The question requires finding the probability of a customer purchasing an imported new Japanese car, which involves calculating the intersection of the probabilities of buying an imported car and a Japanese car. Without additional information to determine if these events are independent or if there is an overlap, an exact probability cannot be provided.

Step-by-step explanation:

The question involves calculating the probability that a customer visited Rac, an automotive dealer, and purchased an imported new Japanese car. Given that 25% bought an imported new car and 45% bought a Japanese car, we are interested in discovering the overlap between these two groups. Since purchasing an imported Japanese car is included in both groups, the probability that a customer bought an imported new Japanese car could be represented by the intersection of these two probabilities.

However, without additional information, such as whether all imported cars are Japanese or if there may be non-Japanese imported cars, we cannot precisely calculate this probability directly. To solve this, we could use the formula for the probability of the intersection of two events if we assume the purchases are independent: P(A and B) = P(A) * P(B), but this would only be accurate if the events are indeed independent, which is not specified in the question. Therefore, due to insufficient data, an exact probability cannot be provided.