00:01
We're looking at a game of roulette, and we want to find the expected value of the game to the player.
00:07
So to find the expected value, i'm going to construct a probability distribution.
00:11
So we'll have x, the possible winnings, and the probability of x, probability of those winnings occurring.
00:18
So maybe you win, in which case you keep the money you pay to play, and you get an extra 280.
00:25
So that's winnings, our profit, of 280.
00:28
If you lose, you just lose your 8.
00:32
So minus 8.
00:34
Probabilities involved here.
00:35
Winning is 1 in 38.
00:38
Losing would then be 37 in 38, because the sum of all possible outcomes, their probabilities, has to be 1.
00:47
Now for part a, the expected value.
00:51
So the expected value of x, also called the mean of this distribution, is calculated by taking each value, multiplying it by its probability and adding them up.
01:02
It's a lot like finding the mean of a frequency table, except we don't have to divide by n, the total frequency, because probabilities sum to one anyway...