00:01
So this question, the three events defined are a, b, c.
00:08
Event a is, it rains today.
00:17
Event b is, you find a taxi, event c is flight is delayed.
00:32
Now, the given probabilities are probability of a, which is equals to 0 .2, probability of b given a, which is equal to 0 .1, probability of 0 .1, probability of c given a which is equal to 0 .75.
00:54
Further, probability of b given a complement represented by a bar which is 0 .60.
01:02
Probability of c given a complement is 0 .125.
01:08
A complement is also represented as a bar.
01:12
Further we can find the probability of a complement which is 1 minus probability of a that will be equal to 0 .8.
01:22
Now coming to part a of the question, in which we have to find the probability of c, that is probability that the flight is delayed.
01:32
So probability of c is same as probability of a multiplied by probability of c given a plus probability of a complement, multiplied by probability of c given a complement.
01:47
So this becomes probability of a is 0 .2 multiplied by probability of c given a, 0 .75, plus probability of a complement 0 .8, multiplied by probability of c given a complement 0 .125.
02:02
So, on solving this, we get this is equal to 0 .25.
02:07
Coming to next part, part b, in which we have to find the probability that it is raining, given that the flight is late.
02:16
Probability that it is raining, probability of a, given flight is late, given c.
02:23
So this will be equals to probability of a multiplied by probability of c given in divided by probability of c.
02:41
So probability of a is equal to 0 .2 multiplied by probability of c given in 0 .75 divided by probability of c which we have calculated above 0 .25.
02:53
So this gives 0 .6 .0.
02:56
Coming to next part part c, in which we have to find the probability of b, that is probability that you find it axi.
03:10
So this becomes probability of a multiplied by probability of b given a plus probability of a complement multiplied by probability of b given a complement.
03:22
So this becomes 0 .2 multiplied by 0 .1 plus 0 .8 multiplied by 0 .6, which is a is equals to these are the given probabilities.
03:38
So this becomes 0 .50.
03:42
Coming to the part, we have to find the probability that you find a taxi given the flight is late.
03:56
So this becomes probability of using the same formula...