00:01
We're looking at a charity raffle, and we want the expected value if you buy a ticket.
00:05
So the expected value of a distribution, e of x, is the mean, they're synonymous, and to get it, you take each possible outcome, multiply by its probability of happening, and add these up.
00:19
It's all like finding the mean of a frequency table.
00:23
So let's construct a distribution here.
00:27
What are the possible outcomes and their probabilities of happening? so the first outcome that might happen is you might win nothing.
00:36
So that would be you just lose one.
00:39
You buy a ticket for a dollar, you don't get anything back.
00:42
There's a prize of 800, so of course you don't get your ticket back, so that's a gain of 799.
00:52
There's prizes of 300, so that's 299.
00:56
There's five prizes of 40, so that's 39, and there's 20 prizes of five, that's four.
01:01
So these are the possible outcomes that you might get.
01:07
Okay.
01:09
Next, what's the probabilities of these happening? well, 5 ,000 tickets have been sold.
01:15
So if there's a single prize of 800, that's a 1 in 5 ,000 chance of happening.
01:20
There are three prizes here, so that's 3 in 5 ,000.
01:24
30, so that's 5 out of 5 ,000 for these, and 20 out of 5 ,000 for these...