00:01
It's given that the probability that only one of three independent events occurs in an experiment is 0 .306.
00:11
Furthermore, we're given the probability of event a is 0 .6, probability of event b is 0 .9, and we are asked to find the probability that event c will occur.
00:23
So the probability of only only one of events a, b, and c occurring can be written as the probability of a and not b, let's use a bar over b to describe the complement of b, and not c, or the probability of or not a, and b occurs, and not c, or not a and not b, but c does occur.
01:12
So this is the probability of one and only one of the three events occurring.
01:19
First term has a occurring, second term has b occurring, third term has c occurring, and in all three terms the other two events do not occur.
01:30
We know this is equal to 0 .306.
01:39
Now because the events are independent and because the events inside the brackets, so these combinations of events, events are mutually exclusive, meaning if one of these occurs and neither of the other two could occur, we can re -express the probability as the probability of a and b0 and c plus the probability of a0 and b and c0 plus the probability of a0 and b0 and c.
02:25
Now for each each of these terms let's calculate them.
02:28
Because the events are independent, the probability of a and b0 and c, sorry this should be c0, the probability of a and b0 and c0 is equal to the probability of a times the probability of b0, which is 1 minus the probability of b, times the probability of c0...