00:01
In this problem, it is said that a company produces a certain type of sophisticated items by three machines.
00:06
And if an item is drawn at random from a day's production and is found to be defective, we need to find the probability that it is not produced by machine c.
00:13
So first of all, let us consider a few events.
00:16
Let a be the event that the item is produced by machine a.
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Let b be the event that the item is produced by machine b.
00:25
Let c be the event that the item is produced by machine c.
00:28
And let d be the event that the item is defective.
00:32
Now, what we want to find is the probability that the item is not produced by machine c given that it is defective.
00:42
So p of c complement given b.
00:44
And that will be equal to 1 minus p of c given d.
00:48
And to find p of c given d, we will use base theorem.
00:53
To use that, we need a set of mutually exclusive and exhaustive events.
00:56
We will use a, b, and c.
00:59
And using those events and using base theorem p of c given d is equal to p of c times p of d given c, divided by p of a times p of d given a plus p of b times p of d given b plus p of c times p of d given c.
01:22
So let us calculate this...