00:01
In this problem, it is said that there are 17 delivery trucks, and out of those 17 trucks, five have brake problems.
00:08
Now, a sample of four trucks is selected at random.
00:11
We need to find the probability that two of those tested have defective brakes.
00:16
Now, the required probability is the number of favorable outcomes divided by the total number of outcomes.
00:21
First of all, consider the total number of outcomes, which you write in the denominator here.
00:26
Now, there are a total of 17 trucks, and out of them any four, are selected at random.
00:32
This can be done in 17c4 ways.
00:35
Here we use c, which represents combination, and we use combination and not permutation in this case because the order of selection of the trucks does not matter.
00:44
Next, consider the number of favorable outcomes, which you write in the numerator here.
00:48
Now, we want to find the probability that two of the trucks tested have defective breaks.
00:53
So the number of favorable outcomes will be the number of ways of selecting four trucks such that two of them have defective brakes.
01:00
So a total of five trucks have defective brakes, and out of them we need to select any two.
01:06
This can be done in 5c2 ways...