00:01
All right.
00:02
So in black up here, i've summarized the information that you were given.
00:08
And then in blue right here, i've calculated one more thing that we're going to need for part b.
00:12
First of all, your information was the probability that the car needs repair is 0 .04.
00:19
The probability that the car was manufactured in the u .s.
00:23
Is 0 .60.
00:25
The probability that a car needs repair and was manufactured in the u .s.
00:30
Is 0 .02.
00:32
Now, for part b, if 60 % of cars were manufactured in the u .s., then 40 % of the cars were not manufactured in the u .s., so p not made in the usa is 0 .4.
00:45
We're going to need that.
00:47
Now, question a, what is the probability that the car needs repair given that it was manufactured in the united states if you read part a? well, this is called a conditional probability.
01:04
And the conditional probability formula really quickly is the probability of a given b is equal to the probability of a and b divided by the probability of b.
01:22
That's your general conditional probability formula.
01:26
So what we're going to do is we're going to put needs repair where a is and manufactured in the u .s.
01:34
Where b is.
01:36
So then the probability that the car needs repair, given that it was manufactured in the u .s.
01:43
Is equal to the probability that it needs repair and made in the u .s.
01:49
Divided by the probability of being made in the u .s.
01:52
So probability of needs repair and made in the u .s.
01:59
Was right here.
02:01
0 .025.
02:03
So that numerator is 0 .025 divided by the probability of being made in the u .s.
02:14
Is 0 .60.
02:16
So if we take 0 .025 divided by 0 .60, we get 0 .025 divided by 0 .60, we get 0 .0 .5.
02:27
042 is your answer to part a.
02:33
Okay.
02:35
Next, if you read part b, it was saying, what is the probability that the car needs repair given that it was not manufactured in the u .s...
