41% 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.
+128408 We have a binomial probabilty here
Exactly three
C(12,4) (.41)^3 (.59)^9 ≈ 29.55%
At least 4 =
1 - C(12,0)(.59)^12 - C(12,1)(.41)(.59)^11 - C(12,2)(.41)^2(.59)^10 - C(12,3)(.41)^3(.59)^9 ≈ 79.5%
Less than 8 =
C(12,0)(.59)^12 + C(12,1)(.41)(.59)^11 + C(12,2)(.41)^2(.59)^10 + C(12,3)(.41)^3(.59)^9 +
C(12,4)(.41)^4(.59)^8 + C(12,5)(.41)^5(.59)^7 + C(12,6)(.41)^6(.59)^6 + C(12,7)(.41)^7(.59)^5 ≈ 93.38%
