00:03
So this problem involves a, i like to explain this using a venn diagram.
00:11
So it tells us the probability that a random new car has an engine fault is 5%, transmission fault is 2%, and probability a new car has one or more of these faults is 6%.
00:28
So i like to do a circle for bad engine.
00:34
That's an engine fault.
00:39
And i like to do overlapping circles.
00:42
The second circle would be a bad transmission.
00:47
And this in -between part where they overlap is your bad engine and a bad transmission.
00:56
So you are told that the probability a new car has one or more of these faults is 0 .06.
01:07
But notice the 5 % and the 2 % adds up to 0 .0 .4 .5%.
01:10
0 .07.
01:12
So that tells me that the in between the intersection, this is 0 .01.
01:21
Bad engine is 5%.
01:24
So bad engine only would be 4 % because notice the 4 % and the 1 % is 5%.
01:31
And a bad transmission is 2%.
01:35
So that tells me since the intersection is 0 .01, this is 0 .01 as well because the bad transmission has to add up to 2%.
01:46
So since these three parts of the overlapping circles add up to 6%, that means 94 % is on the outside because the total area has to add up to 100 % or 1.
02:03
So part a is define the events of interest with notation, the sample space, and the known probabilities.
02:11
So part a, the probability of the probability of of a bad engine only, not banned, but bad.
02:22
Bad engine only is .04.
02:30
The probability of a bad transmission only is .01.
02:40
The probability of a bad engine intersect a bad transmission.
02:48
So that's both.
02:49
A bad engine and a bad transmission is .01.
02:55
So that means the probability of a bad engine.
03:00
Union, so that's or a bad transmission, equals 0 .06.
03:10
That's the addition of all three areas.
03:13
And then the probability of a good engine and or intersect.
03:24
I guess you could say intersect.
03:26
Let's see, erase that.
03:33
Intersect a good transmission equals 0 .94.
03:43
So that would be part a.
03:47
I think i've defined all the individual events.
03:52
So part b, if one of the cars has a faulty transmission, so you know that they have a faulty transmission, the probability has a bad engine.
04:02
So the probability, you're going to write that part b as the probability of a bad engine.
04:12
And this is called conditional probability.
04:14
You know that you're dealing with a bad transmission.
04:20
So bad transmissions are 2%.
04:25
So bad transmission is, look at this big circle, you got 0 .01 and 0 .01 for bad transmissions.
04:35
So that's 0 .01 and 0 .01.
04:37
So that means your denominator is 0 .02...