00:01
Questions we're going to be looking at a lottery system and in this lottery system we've got two different lottery games that for the first lottery game we have 42 different numbers that can be selected okay so numbers 1 through 42 can be selected and there's seven different numbers that need to be chosen out all the numbers are going to be different and the order in which the numbers are chosen doesn't matter just as long as you have those seven numbers so the question is now asking then, what is the probability of winning? so to figure that out, we would have to take what we call a combination.
00:41
Combination is basically what i just described.
00:44
The orders don't matter and the numbers are different.
00:48
So i would plug into my technology or you can also do a series of factorials, but this is much easier just using technology.
00:55
Some combination of 42, since there's 42 numbers.
01:00
And then of those numbers, you're choosing seven.
01:03
So 42 to 7, if you plug that in, you're going to get this number right here.
01:09
It's pretty long.
01:11
It's like 26 ,000, 978 ,000, 328.
01:25
Okay, pretty long number.
01:27
Now, to figure out the probability of winning, only one of these tickets.
01:30
So that's how many possible combinations there are of, like, tickets.
01:35
Only one of them is good.
01:36
Only seven numbers are going to be selected.
01:38
So one time, only one drawing.
01:40
So the probability then of winning as a fraction would be one over 26 ,000, 978 ,328.
01:58
So that's going to be the answer to the first question.
02:02
Now, for the next question, we're looking at a different kind of game.
02:08
Now, for this game, we're looking at it's called a pick four, because you're only going to have four numbers that are going to be selected.
02:16
Now, in a pick four, the digits are going to be repeated this time.
02:21
So the amount of numbers that can be chosen from to win are the same each time.
02:27
So to figure out the chance of winning a pick four, you have to think, okay, so there's four different numbers.
02:36
The chance of getting the first one right is going to be one over ten.
02:40
The chance of getting the second one right is also one over ten, because again, the digits can repeat this time.
02:46
Chance of getting the third one right is one out of ten.
02:49
And the same thing for the fourth number.
02:52
Okay.
02:53
And that is going to equal.
02:56
That is going to equal...