00:01
A box contains five red and five blue marbles.
00:04
So we have five red, five blue.
00:10
We pick two marbles.
00:12
If they have the same colour, we win money.
00:14
If they are different colours, we lose money.
00:16
We want the expected winnings and the variance.
00:20
So first i'm going to make a probability distribution representing the amount we win.
00:25
So x could be 1 .1 or it could be minus 1.
00:29
Now, what are the probabilities associated with this? first of all, what's the probability of getting two of the same colour? so either red red or blue blue.
00:40
So for red red, the probability the first marble is red is 5 out of 10.
00:45
There are 10 marbles, 5 of them are red.
00:48
Now we put that marble to one side and pick out a second marble.
00:53
There are only 9 left.
00:54
Out of these, 4 are red.
00:57
So we we get 2 out of 9.
01:01
For blue, it's the same idea, 5 out of 10, 5 blue, 4 out of 9, also 2 out of 9.
01:07
If we add those up, we get 4 over 9 is the probability of picking 2 of the same colour...