Question

Three car brands A, B, and C have all the market share in a certain city. Brand A has 20% of the market share, brand B has 30%, and brand C has 50%. The probability that a brand A car needs a major repair during the first year of purchase is 0.05, the probability that a brand B car needs a major repair during the first year of purchase is 0.10, and the probability that a brand C car needs a major repair during the first year of purchase is 0.15. a. What is the probability that a randomly selected car in the city needs a major repair during its first year of purchase? b. If a car in the city needs a major repair during its first year of purchase, what is the probability that it is a brand A car? Two events A and B have the following probabilities: P[B] = 1/4 P[A ? B] = 3/8 P[A ? B] = 3/8 Compute P[B|A]?

          Three car brands A, B, and C have all the market share in a certain city. Brand A has 20% of the market share, brand B has 30%, and brand C has 50%. The probability that a brand A car needs a major repair during the first year of purchase is 0.05, the probability that a brand B car needs a major repair during the first year of purchase is 0.10, and the probability that a brand C car needs a major repair during the first year of purchase is 0.15.

a. What is the probability that a randomly selected car in the city needs a major repair during its first year of purchase?
b. If a car in the city needs a major repair during its first year of purchase, what is the probability that it is a brand A car?

Two events A and B have the following probabilities:

P[B] = 1/4    P[A ? B] = 3/8    P[A ? B] = 3/8

Compute P[B|A]?

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Added by Howard F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kari Hasz

06/21/2022

Step 1

- Probability of brand A needing a major repair: 20% * 0.00 = 0.00 - Probability of brand B needing a major repair: 30% * 0.10 = 0.03 - Probability of brand C needing a major repair: 50% * 0.15 = 0.075 - Total probability = 0.00 + 0.03 + 0.075 = 0.115 Show more…

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Three car brands A, B, and C have all the market share in a certain city. Brand A has 20% of the market share, brand B has 30%, and brand C has 50%. The probability that a brand A car needs a major repair during the first year of purchase is 0.05, the probability that a brand B car needs a major repair during the first year of purchase is 0.10, and the probability that a brand C car needs a major repair during the first year of purchase is 0.15. a. What is the probability that a randomly selected car in the city needs a major repair during its first year of purchase? b. If a car in the city needs a major repair during its first year of purchase, what is the probability that it is a brand A car? Two events A and B have the following probabilities: P[B] = 1/4 P[A ∩ B] = 3/8 P[A ∪ B] = 3/8 Compute P[B|A]?

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00:01 Three car brands, a, b, and c, all have the market share in a certain city.

00:05 Brand a has 20%, brand b has 30%, and brand c has 50 % of the market share.

00:16 The probability that a brand a car needs a major repair during the first year of purchase is 0 .05.

00:25 The probability that brand b needs a repair, and the first year of purchase is 0 .10, and the probability that c needs a repair in the first year is 0 .15.

00:38 What is the probability that a randomly selected car in the city needs a major repair during its first year of purchase? so i'm just going to put that as probability of repair.

00:47 And that's going to be multiplying each of these branches and then adding up those numbers.

00:54 So 0 .2 times 0 .05 is 0 .01.

00:58 Then we'll add 0 .3 times 0 .10, which is 0 .01 .1 .3 times 0 .10, which is 0.

01:02 0 .03 and 0 .5 times 0 .15, which is 0 .075, for a total probability of 0 .115.

01:12 Next, we're going to find the probability.

01:15 If a car in the city needs a major repair during its first year purchase, what's the probability that it is a brand a car? so that would be the probability that it is car a, given that it needs repairs.

01:30 So first we're going to find the probability of a and r, which is 0 .2 times 0 .05, which is equal to 0 .01.

01:38 And then we're going to divide it by the probability of r, which we already found to be 0 .115...

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