00:01
In this problem, it has said that three cooks, a, b, and c, bake a special cake.
00:04
We have been given the respective probabilities that the cake fails to rise, and we are also given information about which cook bakes how many of the cakes in the restaurant.
00:15
Now, what we need to determine is the proportion of failure, which is caused by the cook a.
00:23
So let us consider a few events.
00:26
Let us consider a to be the event that cook a bake the cake, let b.
00:30
Be the event that b bake the cake, let's c be the event that c bake the cake, and let us consider f could be the event that the cake failed to rise.
00:38
Now we want to find the proportion of failure that is caused by a.
00:42
So what we want to find is the probability that a cake was baked by a given that that cake failed to rise.
00:49
This is the probability we need to find.
00:51
And to do that, we will use base theorem.
00:55
Now to use base theorem, we need a set of mutually exclusive and exhaust.
01:01
Exhaustive events, and in this case, we will use the events a, b, and c.
01:05
So using those three events and using base theorem, p of a given f is equal to p of a times p of f given a, divided by p of a times p of f given a plus p of b times p of f given b, plus p of c times p of f given c.
01:30
So what is p of a? that is the probability that the cake was baked by a.
01:34
Now a bakes 50 % of the cake, so this will be 50%...