00:01
In this problem, we have been given a sample space and some probabilities.
00:04
Now, first of all, we need to find the probability assignment for the probability space when 03, 04, and 05 all have the same probability.
00:13
Now, recall that if we have a sample space and we add the probabilities of all of the sample points, then that will be equal to 1.
00:22
So the probability of 01 plus the probability of 02 plus the probability of 03 plus the probability of 04 plus the probability of 05, this should be equal to 1.
00:39
Now the probability of 01 is given to be 0 .2 and the probability of 02 is given to be 0 .32.
00:47
And it said that 0304 and 05 all have the same probability, so let that be x.
00:52
So we have x plus x plus x this is equal to 1.
00:55
So we have 0 .52 plus 3x this is equal to 1.
01:00
And that will imply that 3x is equal to 1 minus 0 .52, which is 0 .48.
01:07
And this means that x is equal to 0 .48 by 3, which is 0 .16.
01:13
So what do we end up with? what is our probability assignment? for 01, it is given to be 0 .2.
01:20
For 02, it is given to be 0 .32, and for 03, we will have 0 .16.
01:28
For 04, we will have 0 .16.
01:31
And for 05, we will have 0 .16.
01:34
So this is our required answer.
01:38
Next, we need to find the probability assignment if the probability of 0 .5 is 0 .2 and 03 has the same probability as 04 and 05 combined.
01:48
So once again, if we add all of the probabilities, we will get one.
01:51
Now, the probability of 01 is 0 .2, the probability of 0 .2 is 0 .32...