00:01
For this problem, we are told to consider a double ids with system a and system b.
00:05
We're told that if there is an intruder, system a sounds an alarm with probability 0 .9.
00:11
And system b sounds an alarm with probability 0 .95.
00:14
We then told that if there is no intruder, the probability that system a sounds an alarm, i .e.
00:19
A false alarm, is 0 .2.
00:20
And the probability that system b sounds an alarm is 0 .1.
00:24
In part a, we are asked to use symbols to express the four probabilities given.
00:29
So what i'll do is write that the probability of alarm a going off, that's event, i'll call that event a, given that there is an intruder, so p of a given i is equal to 0 .9, and then we have p of b given i equals 0 .95.
00:50
Then we'd have for the false positives, p of a given i complement, so no intruder equals 0 .2, and p of a given, or p of b given i, c, one moment here, p of b given i complement, equals 0 .1.
01:10
Then for part b, we are asked, if there is an intruder, what is the probability that both systems sound an alarm? so this would be the probability of essentially a and b given i.
01:28
Now, we can find this by evaluating the probability of a given i plus the probability of b given i minus the product of those probabilities.
01:42
That would be the product or the probability of their intersection given that, or essentially given that there is an intruder, and we are making the assumption that the two alarms going off would be independent...