00:01
So we have all this information given about three different events.
00:04
We have rain, we have the temperature exceeding 75 degrees fahrenheit, and we have a major thunderstorm.
00:13
So we want to go through and make a venn diagram.
00:16
And i started just to make a venn diagram by showing three circles.
00:21
Let me just draw a little picture here.
00:22
I drew rain, temperature exceeding, and then i drew this for the thunderstorm.
00:30
I found from this probability right here that we know that if a thunderstorm happens, we know that there has to be rain.
00:41
So this there is, if the thunderstorm happens, this part of the venn cannot exist.
00:50
That has to go away and this would also be not rain.
00:54
So my diagram looks like this, that i have my event of raining, and outside that circle is not raining.
01:02
I have the temperature being higher than 75 degrees and that intersects with not raining.
01:09
And then the thunderstorm has to be contained within the rain.
01:14
Because the thunderstorm, if the thunderstorm takes place, there is rain.
01:21
So this is the thunderstorm taking place and i didn't have to, i could draw it in the center here.
01:29
But if the thunderstorm takes place, then we know it is raining.
01:34
So it can't be outside of that rain circle.
01:39
So now let's see, where did i get all these probabilities? so let's go back and label.
01:43
So we know that we have the intersection of the temperature being 75 degrees and not raining.
01:54
Well, so it has to be here and outside that circle.
01:57
This had to be 45%.
01:59
So we've used that.
02:01
We've used this.
02:03
Now we need the intersection of a thunderstorm happening and the temperature being 75, being 5%.
02:10
And a thunderstorm happening and the temperature being 75, that intersection is right here and we know it has to be raining.
02:19
So that is 0 .05.
02:20
That's this one.
02:22
So we go to the next part and we know that these two add up to 50 % and we know the probability that the temperature is 75 degrees.
02:34
These two add up to 50 % and the temperature being more than 75 degrees is 60%.
02:40
So this had to be 10%.
02:42
So that's utilizing this piece of information.
02:47
Then we could find that the probability of a thunderstorm was 10%.
02:52
We already had this little component.
02:54
So this had to be 5 % as well.
02:57
And then adding these all up, that's 10 % plus 10 is 20%.
03:02
And we know the probability of rain is 35%.
03:06
So this had to be 15%...