00:01
For this problem, to begin in part a, we have that the probability of a and b can be calculated using our typical rules of probability as the probability of b minus the probability of a or b.
00:18
So, using the data that's given to us, probability of a is 0 .4, pb is 0 .7, and pa or b is 0 .9.
00:28
So, we find the probability of a and b is 0 .2.
00:34
For part b, probability of a complement and b is going to be equal to, well, similar idea, probability of a complement plus probability of b minus...
00:49
Now, actually, i'll back up a second here.
00:52
At this point, it does become a little bit more complicated.
00:57
In this case, we can find the probability of a complement and b, by taking the probability that a does not occur, so that's 1 minus p of a, multiplying it by the probability that b does occur.
01:12
So we can see that that's going to be 1 minus 0 .4, gives us a result of 0 .6, and probability of b occurring is 0 .7.
01:22
So we'd have 0 .6 times 0 .7 for a result of 0 .42.
01:27
Then for part c, probability of a minus b, this can be expressed equivalently as the probability that a occurs, and b does not occur.
01:44
So, that's going to be, well, probability that a occurs, we know is 0 .4.
01:49
Then we multiply that by 1 minus the probability that b happens, so 1 minus 0 .7, which gives us a result of 0 .12.
01:58
For part d, probability of a complement minus b is equal to the probability of a complement and b complement, which, using demorgan's laws, can be thought of as the probability of the complement of a or b, which is 1 minus the probability of a or b.
02:26
And we're given that the probability of a or b is 0 .9.
02:32
So we have the probability of a complement minus b is 0 .1...