00:01
Okay, we throw a fair die.
00:02
X is the outcome, either one, two, three, four, five or six.
00:07
And the first thing i'll do, the chance of x happening.
00:12
Well, it's the same all the way down.
00:14
There's a one -sixth chance of getting any of the results.
00:20
It's a fair die.
00:22
And in part a, i want to work out the expectation if the game costs $1 to pay.
00:31
So let's do this list here.
00:37
$1 to play.
00:40
So how much do you win then if you pay $1 and you get back in dollars the number of dots on the dial? so if one dot is showing, then you break even.
00:57
Zero.
00:58
You paid $1, got back $1.
01:01
Here what you have, you've gained $1.
01:06
Here you've gained $2.
01:08
Here are $3, 4, and 5.
01:13
So you pay 1, get back, number of dots.
01:18
So here then, the expectation then will be 1 times 0, sorry, 1 6 times 0 is 0.
01:33
1 6 times 1 .6 times 1 .6 times 2 times 3, 4 6 here, 4 6 here and 1.
01:45
Six times five here five sixth as your expectation so add this up five nine and twelve thirteen fifteen over six which divide by three top and bottom five and two which implies you're going to win two dollars and fifty cents overall if you keep playing the game for a long time so clearly that game won't be in the casino now part b we are paying or paying $2.
02:30
So let's do it over here, $2 to play.
02:38
So here then what i'm going to win is negative $1.
02:46
I paid $1, i paid 2, got back 1.
02:52
Here will be 0 because i'm getting a score 2, i get back $2, i've paid $2 already.
03:01
So here it's 1, 2 ,000.
03:02
Two, three, and four.
03:06
So same idea...