00:02
Let a be the event of raining tomorrow and b be the event of raining day after tomorrow.
00:35
Now, from the question we can see that whenever it rains on the first day, then the probability of raining the next day is 1 over 3.
00:50
When given that a has happened the probability of b is given so probability of b given a is 1 over 3 and the probability of raining on the next day whenever a complement has happened that is whenever it is not raining tomorrow the probability of raining day after tomorrow is also given so probability of b given given complement has also happened is 1 over 6 and also we are given with probability of a that is probability of raining tomorrow is given to be 1 over 5 so we are supposed to do two supposed to do three things number one we have to check whether what is the probability that it will rain day after tomorrow so we are asked to find what is the probability of b and question a is we have to draw a tree diagram of all the possibilities and question b is about what is the probability that it will rain on one of the days so we have to combine these two things so we have to find probability of a union b that is a is raining tomorrow b is raining day after tomorrow so a union b gives us the probability of raining on either of two days.
02:29
So let's start.
02:30
So to find probability of b, we use the total probability formula.
02:34
So probability of b is equal to probability of b given a times probability of a plus probability of b given a complement times probability of a complement.
02:51
So probability of b is about to be found.
02:55
So probability of a is not a...
02:58
B given a is 1 over 3 so 1 over 3 times probability of a is given 1 over 5 plus probability of b given a compliment is 1 over 6 times probability of a complement we can find a complement from probability of a so probability of a compliment is 1 minus probability of a so this is one minus 1 over 5 which is 4 over 5 so this is 1 by 15 plus 4 by 30 so we can find that to be 6 by 30 or 1 by so probability of b is found so this is equal to 1 by 5.
03:43
So to answer question a we are supposed to do a tree diagram.
03:49
So three diagram so we are supposed to find whenever it is raining day after tomorrow.
03:59
So, it can happen that it rains tomorrow or it does not rains tomorrow.
04:11
So, we have two events, a and a complement...