00:01
In this problem, it is said that a girl selects a ball by first picking one of two boxes at random and then selecting a ball from this box.
00:10
We need to find the probability that the girl picked a ball from the second box if she has selected an orange ball.
00:17
Now, considering the information given in the problem, let us consider a few events.
00:22
Let b1 be the event that the girl selects the first box.
00:26
Let b2 be the event that the girl selects the second box.
00:30
And let o be the event that the girl selects an orange ball.
00:35
Now, what we need to determine is the probability that the girl picked a ball from the second box, given that she has selected an orange ball.
00:45
So we need to find p of b2 given o.
00:47
Now, in order to do this, we will use base theorem.
00:53
Now, to use base theorem, we need a set of mutually exclusive and exhaustive events.
00:58
So in this case, we will use the events b1 and b2.
01:02
These are mutually exclusive because the girl will select only one box.
01:07
She cannot select both boxes simultaneously.
01:12
And they are exhaustive because these are the only two boxes.
01:15
So the girl will either select the first box or the second box.
01:20
So one of these events must happen.
01:22
So these two are mutually exclusive and exhaustive, and so we can use these two events to use base theorem.
01:28
And according to base theorem, p of b2 given o will thus be p of o given b2 times p of b2 divided by p of o given b1 times p of b1 plus p of o given b2 times p of b2.
01:48
So consider p of o given b2...