00:02
A committee of size 4 is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 from the sales department, and 1 chartered accountant.
00:20
We are asked to find the following probabilities for forming these committees.
00:24
For part a, there must be 1 from each category.
00:27
So here we are going to assume that each person is equally likely to be chosen for the committee.
00:35
To calculate the probability that there is 1 from each category, we know there are 3 in the production department, so there are 3 choose -one ways to pick 1 person from the production department, 4 choose -one ways to pick somebody from the purchase department, 2 choose -one from the sales department, and 1 choose -one from the chartered accountant.
01:04
We divide this by the total number of ways of picking 4 people out of all of these people.
01:09
So if we add up all of the people, 3, 4, 2, and 1, this gives us a total of 10.
01:18
There are 10 choose -four ways to pick 4 people out of these 10.
01:26
And this comes out to approximately .1143.
01:30
So the probability that there is 1 person from each department is .1143.
01:37
For b, we want the probability that there is at least 1 from the purchase department.
01:43
The easiest way to solve this is to take 1 minus the probability that there are none from the purchase department.
02:01
So in terms of the probability that none are from the purchase department, the number of ways of picking none from the purchase department, there is a total of 4 in the purchase department, so there are 6 people who are not in that department...