00:01
In this problem we have two routes from the hospital to the emergency.
00:05
Now the probability of any of these intersections being blocked is 0 .1.
00:18
And for part a we are asked for the probability that there will be one open route from the hospital to the emergency.
00:34
So we can say that's the probability of an open route by willow street or an open route by briarwood road.
00:50
And using probability theory that's equal to the probability that there's an open route through willow.
00:54
Plus the probability that there's an open route through briarwood minus the probability of an open route through both of these streets.
01:25
So or is union and is intersect.
01:30
For the probability that there's a route through willow that is open, it's the probability that the first intersection is open or clear, times the probability that the second intersection is clear.
01:47
And the same can be said for the probability for briarer.
01:49
And the probability that willow and breyerwood are both open is the probability that all four intersections are clear.
02:07
And that comes out to .9639.
02:13
And for part b we are asked for the probability mass function for the number of routes that are open.
02:23
So it can be anywhere from zero to two roots open.
02:32
Now first the probability that none are open is equal to 1 minus the probability that at least 1 is open, which is 1 minus .9639.
03:02
Now the probability that x is exactly equal to 1 equals the probability that willow is clear but briarwood is blocked or vice versa.
03:16
So for the first case, willow is clear is .9 times .9 times the probability that briarwood is blocked, which is .1 times .1.
03:30
If you were right it this way first.
03:38
We'll call that briarwood prime.
03:39
When briarwood is blocked...