00:01
So the first requirement that we need to keep in mind here is that since we have our sample space is events 1, 2, 3, and 4, we have to have that the probability of any one of those events happening, so the probability of something occurring has to be equal to 1.
00:22
You have to be able to guarantee that the probability of something happening is 1, which then in turn means that we have to have, we have to have that the probability of 1 plus the probability of 2, plus the probability of 3, plus the probability of 4 has to be equal to 1.
00:44
And now we can start using the relationships between the different probabilities as indicated.
00:51
So, let's see here.
00:56
We have that p of 2 is equal to 3 times p of 3, and we have that p of 2 is equal to 3 is equal to 4.
01:06
Times p of four, and we have that p of two is equal to p of one minus one over eight.
01:18
So what this means is that we can express the event, or we express, pardon me, we can express the probabilities of each one of the other events in terms of the probability of event two.
01:32
So we have p of one equals p of two plus one over eight, we have p of four must be equal, to p of 2 over 4 and we have p of 3 must be equal to p of 2 over 3 which means that when we put all of this together we should have p of 2 plus 1 over 8 plus p of 2 over 3 plus p of 2 over 4 must be equal to 1 or if we subtract 1 over 8 from both sides so we get everything on the left hand side in terms of p of 2 then we have that the sum of all those probabilities must be equal to 7 over 8...