Question

42​% of a certain​ country's voters think that it is too easy to vote in their country. you randomly select 12 likely voters. find the probability that the number of likely voters who think that it is too easy to vote is​ (a) exactly​ three, (b) at least​ four, (c) less than eight.

Answer 1

A) 0.1211
B) 0.3889
C) 0.9782

Explanation:
A)  We use a binomial distribution for this:
$_nC_r(p)^r(1-p)^{n-r} \\ \\_{12}C_3(0.42)^3(1-0.42)^{12-3}=_{12}C_3(0.42)^3(0.58)^9=0.1211$

B)  Using a graphing calculator, we find the sum of the binomial probabilities from 0 up to (not including) 5:  0.6111.  Now subtract this from 1, since we want everything greater than or equal to 4:  1 - 0.6111 = 0.3889

C)  Using a graphing calculator, we find the sum of the binomial probabilities from 0 up to (not including) 8:  0.9782