Question

In a population where 81 % of voters prefer Candidate A, an organization conducts a poll of 18 voters. Find the probability that 12 of the 18 voters will prefer Candidate A.

Answer 1

0.069664≅0.070

Step-by-step explanation:

the question in based on binomial probability which means the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes p and q and p+q=1

let probability of choosing candidate A be p

and probability of choosing candidate B be q

In question p=0.81 and q=0.19

n be total number of voters=18

x be number of successes

then P(x=x)=
`\binom{n}{x}p^(x)q^(n-x)`

P(x=12)=
`\binom{18}{12}0.81^(12)0.19^(6)`

= 0.069664≅0.070

therefore the probability of 12 voters out of 18 voting candidate A is 0.070