00:01
In this question, we're given that there are two pumps.
00:04
Probability only the older pump will fail is 0 .25, and probability only the newer pump will fail is 0 .2.
00:12
And the two pumps, they fail independently of one another and are connected in parallel.
00:19
So i'm going to let event a be the older pump will fail, and event b, the newer pump will fail.
00:27
Now, we want to find probability the pumping system.
00:30
Will fail on any given day.
00:32
That means we want to find probability both palms will fail.
00:36
That means both event a, n.
00:39
Now in probability n is times, set notation is intersect, or is plus set notation is union.
00:46
So a, n is intersect, b.
00:50
So we want to find probability a intercept b.
00:54
But first let's draw a venn diagram.
00:59
I'm going to draw event a here.
01:00
That means palm a will fail.
01:02
And event b here means palm b will fail.
01:05
So we're interested to find event a intercept b, which is in the middle, both events happen at the same time.
01:14
Okay, now we have that probability only the older pump will fail.
01:20
That means probability a only is 0 .25.
01:27
Now a only is down here.
01:31
So this part here is 0 .25.
01:35
And we have probability only the newer palm will fail is 0 .2.
01:39
That means probability even b only.
01:44
That means that is 0 .2...