00:01
So for figuring this out, the first step that we're going to want to take is to determine the total number of different possible outcomes.
00:07
We know on each coin we have two different possibilities, and we're flipping three coins.
00:14
So we would have two cubed different possibilities, or eight different possibilities in total.
00:21
We know that the number of ways to get three heads would just be one.
00:29
There's only one way to get three heads with three coins, which is heads, heads, heads.
00:34
So we have that the probability of three heads is equal to one over eight.
00:44
So when we look then at the distribution for our different payouts, where we have x is the payout and then the probability of that payout, we would win $5 if we succeed.
00:57
So that's probability 1 over 8, and we lose $2 if we fail.
01:02
Which would have probability 7 over 8.
01:06
So to find the expected value, to me, or to us, of the game, that would be equal to, let me bring down my software, it's always the product of each outcome, multiplied by its probability, so it's 5 times 1 over 8, all added together.
01:29
So we'd have 5 times 1 over 8 plus negative 2 times 7 over 8, so we'd have that the expected value is equal to negative 9 over 8.
01:40
So we then have that we would expect to lose money...