Question

The probability that a visit to a particular car dealer results in neither buying a second-hand car nor a Japanese car is 55 %. Of those coming to the dealer, 25 % buy a second-hand car and 30 % buy a Japanese car. (Hint: Draw Venn diagram) a) What is the probability that a visit leads to buying a second-hand and Japanese car? b) What is the probability that a visit leads to buying a Japanese car if is known that bought car is a second-hand one? c) Are events of buying Japanese and second-hand cars independent? (Justify your answer)

          The probability that a visit to a particular car dealer results in neither buying a second-hand car nor a Japanese car is 55 %. Of those coming to the dealer, 25 % buy a second-hand car and 30 % buy a Japanese car. (Hint: Draw Venn diagram)

a) What is the probability that a visit leads to buying a second-hand and Japanese car?




b) What is the probability that a visit leads to buying a Japanese car if is known that bought car is a second-hand one?






c) Are events of buying Japanese and second-hand cars independent? (Justify your answer)

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The probability that a visit to a particular car dealer results in neither buying a second-hand car nor a Japanese car is 55 %. Of those coming to the dealer, 25 % buy a second-hand car and 30 % buy a Japanese car. (Hint: Draw Venn diagram)

a) What is the probability that a visit leads to buying a second-hand and Japanese car?

b) What is the probability that a visit leads to buying a Japanese car if is known that bought car is a second-hand one?

c) Are events of buying Japanese and second-hand cars independent? (Justify your answer)

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joanna Quigley

07/06/2022

Step 1

We are given the probabilities of various outcomes when visiting a car dealer. Specifically, we know that: - The probability of not buying a second-hand car nor a Japanese car is 55%. - The probability of buying a second-hand car is 25%. - The probability of Show more…

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The probability that a visit to a particular car dealer results in neither buying a second-hand car nor a Japanese car is 55 %. Of those coming to the dealer, 25 % buy a second-hand car and 30 % buy a Japanese car. (Hint: Draw Venn diagram) a) What is the probability that a visit leads to buying a second-hand and Japanese car? b) What is the probability that a visit leads to buying a Japanese car if is known that bought car is a second-hand one? c) Are events of buying Japanese and second-hand cars independent? (Justify your answer)

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Transcript

00:01 So we're looking at visits to a car dealer.

00:04 And we're going to be drawing a venn diagram, as it recommends.

00:08 So we've got second -hand cars and japanese cars.

00:13 Of course, you can have both.

00:18 If these are actually independent, we will find out soon enough.

00:22 Hypothetically, you should be able to get a second -hand japanese car.

00:26 We're going to see if that's actually happening here.

00:29 So the probability, but you get neither, so buying no car at all, buying some other type of car is 55%.

00:37 So that's outside of the diagram.

00:40 It's, let's say this circle here is the japanese cars, and this circle here is the second -hand cars.

00:49 Okay, 25 % by second -hand, 30 % by japanese cars.

00:55 So this entire circle, including this bit in here, is 30%.

01:01 This entire circle here is 25%.

01:06 Are they independent? they cannot be.

01:09 Because if we add up all of these probabilities, we get over 100%.

01:12 There has to be some overlap here.

01:16 So, what is the probability that they buy a second hand and japanese car? well, we've got 55 % here.

01:26 We should really only have 45%.

01:28 So we do have some overlap.

01:31 So if we put in 10 here, that would make this 20 and this 15...

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