00:01
We can use the binomial distribution to solve this problem since each voter can either prefer candidate a, b, or no preference.
00:15
The probability that a randomly chosen voter prefers candidate a is 0 .4, the probability of preferring b is 0 .1, and no preference 0 .5.
00:24
If we let x be the number of voters in a sample of 10 who prefer candidate a, y prefer candidate b, and z no preference, then x, y, and z are all binomial random variables with parameters of n equals 10 and p equals 0 .4, n equals 10 and p equals 0 .1, and n equals 10 and p equals 0 .5.
01:02
The pnf of a binomial distribution is the number of ways that it could be selected.
01:11
So like if x equals k, then it's n choose k to the 10.
01:25
The pnf of x is 10 choose k times 0 .4 to the k, and then the difference of 1 which is 0 .6 to the 10 minus k.
01:46
Those exponents need to add to 10.
01:52
The pnf of y would be 10 choose k times 0 .1 to the k times 0 .9 to the 10 minus k.
02:11
And the pnf of z would be 10 choose k times 0 .5 to the k times 0 .5 to the 10 minus k.
02:25
To find the probability that exactly k voters prefer candidate a exactly, j voters prefer candidate b, and the remaining have no preference...