00:01
All right, problem four, we have three vehicles taking a freeway exit at the end.
00:07
They can either turn right, left, or go straight.
00:10
And they want us to list all the outcomes in the event that all three vehicles go in the same direction.
00:17
Okay, so those outcomes would be first car left, second car left, third car left, four.
00:25
First car right second car right third car right or lastly first car straight second card straight third card straight all right um b list the uh the outcomes in the event that b that they all go in different directions okay so we need to do is mess around with the order of r's l's and s's all right so i'm gonna say the first car turns right so that means the second car can turn left and the third one straight but i could also take these first last two and reverse the order so we could have right for the first car and straight for the second car the left for the third so that's all of the possibilities for when the first car goes right okay or the first car goes right so now i'm going to do the same thing this time the first car is going to go left.
01:31
So then the other two might go right and straight, or the other two might go straight and right.
01:39
So you see how i'm just switching the order of the second two.
01:42
So those are all the possibilities where the first car goes left.
01:47
The last is if the third car goes straight.
01:51
Oh, sorry, this would be left.
01:58
So straight with right left, straight with left right.
02:06
Okay, and we've got all six possibilities.
02:11
Okay, see, list all outcomes in the event that see that exactly two of the three vehicles turn right.
02:24
Okay, so two of the three turn right.
02:28
Okay, so i'm going to start out with, let me see, the first one goes right, and then the second one goes well how should so right left right okay then we can follow that up with right straight right and then right right right straight now the only place left to put the two two ours for this one right here would be to put them in the last two positions so that would be lrr or straight rr.
03:51
Okay, so that's the probability that two of the three vehicles turn right.
04:03
Okay, so now in d they switch it up and they say, what if you list all the outcomes where exactly two vehicles go in the same direction.
04:15
So instead of being right, okay, you would have a number.
04:19
Another set of these, another set of these where all the r's would turn into l's and the l's would turn into r's.
04:33
And then you'd have another set of those, right, where the r's turn into s's, go straight, and the straights turn into rights.
04:45
So basically what you have is three times this set right here.
04:50
For a total of 18 outcomes.
04:53
And again, if you wanted to actually make the list, that's how you would do it.
04:58
You just copy this list down but interchange the r with the l's and the r's with the s's.
05:05
So that we'd have two right turn, a set where there's two right turns, a set where there's two left turns, and a set where there's two straights.
05:14
Okay.
05:16
Last, list the outcomes for these different things.
05:20
It's a long problem...