00:01
This problem, we were told that we haven't earned with three green balls, two blue, and four red.
00:12
And we would like to find the probability that whenever we choose five at random, then we have both of the blue and at least one of the red.
00:29
Now, in finding this probability, since we want at least one red, this is equal to one minus the probability of two blue, and zero red.
00:39
And that just comes from using our complement law.
00:43
Now this is just our multinomial distribution, and so we have one minus.
00:48
Now we have a total of nine, and we want two blue, no red, and since we're choosing five total, that means we need all three of the green.
01:01
Now you also notice that the probability of a green on one draw is three out of nine.
01:09
We have three green and nine total.
01:11
The probability of red is four out of nine, four red, nine total.
01:17
And the probability of a blue is two out of nine.
01:21
Now back down here, since we want two blue, we'll have two nines raised to the second...