00:01
In this problem, we have been given certain probabilities about a person when whether he's late to work or not, and we are also given the probability that it will rain tomorrow.
00:12
Using this information, the first probability that we need to determine is the probability that joe is early tomorrow.
00:20
So we need to find the probability that he's early.
00:23
Now, there are two possible cases in which he is early.
00:26
One is that it is rainy and he's early, and the other is that it is non -rainy and he's early.
00:31
Still early.
00:32
Now first of all, let us determine the probability that he is early on a rainy day.
00:37
Now, the probability that it will be rainy is 0 .7.
00:41
And the probability that he is late to work on a rainy day is 0 .3.
00:49
So the probability that he is early will be 1 minus 0 .3.
00:54
So the probability that on a rainy day, joe is early will be obtained by using the multiplication rule of probability.
01:00
So we multiply these two.
01:03
Next, we have the option of it being a non -rainy day.
01:07
Now, the probability that it will rain is 0 .7.
01:10
So the probability that it will not rain is 1 minus 0 .7.
01:14
With this, we multiply the probability that he will be early.
01:19
Now, he's late with probability 0 .1 on a non -rainy day...