00:01
In this problem, we have been given a tree diagram and we need to determine certain probabilities.
00:06
The first probability we need to determine is the probability of c given a.
00:10
That is the probability of the event c happening given that a has already happened.
00:15
So if we have a look at the tree diagram, we can see that a happens with the probability of 0 .7.
00:21
And once a has happened, c occurs with the probability of 0 .25.
00:26
So the probability of c given a, that will be 0 .25.
00:31
Next we need to find the probability of b given b.
00:34
This is the probability of the event b happening given that the event b has already occurred.
00:40
So we can see that b occurs with the probability of 0 .3 and once b has occurred, b occurs with the probability of 0 .3 -5.
00:48
So this is the required answer.
00:50
Next we want the probability of a intersection c.
00:54
So this we will use the multiplication rule of probability.
00:57
According to that, this will be equal to p of a times p of c.
01:01
Given a.
01:02
The probability of a occurring can be seen from the diagram to be 0 .7, and p of c given a is 0 .25, which we already calculated.
01:12
And if we calculate this, we end up with 0 .175, that's the required probability...