Tricky Stats Probability?

Question

40% of the students are REGISTERED to vote. 60% of those prefer candidate A and 40% prefer candidate B.

60% are NOT REGISTERED to vote. 30% prefer candidate A and 70% prefer candidate B.

if there are 10 REGISTERED voters, what is the probability of getting 2-5 (two to five) votes for candidate B? (there is only one answer)

any help would be appreciated. thanks in advance

Answer 1

Let X be the number of votes candidate B gets.

X has the binomial distribution with n = 10 trials and success probability p = 0.40.

In general, if X has the binomial distribution with n trials and a success probability of p then
P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)
for values of x = 0, 1, 2, ..., n
P[X = x] = 0 for any other value of x.

this is found by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures.

the mean of the binomial distribution is n * p
the variance of the binomial distribution is n * p * (1 - p)


Find P(2 ≤ X ≤ 5)
= P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
= 0.1209324 + 0.2149908 + 0.2508227 + 0.2006581
= 0.787404

Answer 2

First of all, the second paragraph is irrelevant to this problem.
Secondly and more importantly, you say there are 10 registered voters. If that's the total no. of registered voters, then 6 of them prefer candidate A. So candidate B will get 4 votes, hence P(2-5 for B) = 1.

If however you meant that 10 registered voters were selected from a large sample, then it's a binomial problem.
p = 0.4
n = 10
Use the binomial formula to find P(X = 2,3,4,5)
You should get 0.7874

Answer 3

don't believe in statistics or exit polls--I would wait until the actual votes are counted before answering this one, the day after the election.