SOLUTION: A poll shows that 70% of all voters approve of the mayor's work. On three separate occasions a pollster selects a voter at random. What is the probability that on exactly one of th

Algebra ->  Probability-and-statistics -> SOLUTION: A poll shows that 70% of all voters approve of the mayor's work. On three separate occasions a pollster selects a voter at random. What is the probability that on exactly one of th      Log On


   



Question 1195870: A poll shows that 70% of all voters approve of the mayor's work. On three separate occasions a pollster selects a voter at random. What is the probability that on exactly one of these three occasions the voter approves of the mayor's work?

The explanation on aops was not detailed enough for me, especially the part where it says %280.7%29%280.3%29%5E2%29
https://artofproblemsolving.com/wiki/index.php/2008_AMC_10B_Problems/Problem_17

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if given that 70% of all voters approve of the mayor's work, then 30% of all voters disapprove of the mayor's work

using binomial distribution formula

nCx+%2A+P%5Ex+%2A+%281+-+P%29%5E%28n+-+x%29
we find the number of ways only 1 person approves (+nCx+) of the mayor multiplied by the probability 1 person approves(+P%5Ex+) and+2 people disapprove ( %281+-+P%29%5E%28n+-+x%29 )


the number of ways only 1 person approves is x%7D%7D+of+%7B%7B%7Bn%7D%7D+persons%0D%0A%0D%0A%7B%7B%7BP=probability (is given)

3C1+%2A0.7%5E1%281-0.+7%29%5E%283-1%29 since +3C1=3%21%2F%28%283-1%29%21%2A1%21%29=3
=3%2A0.7%5E1%28.+3%29%5E2
=3%2A0.+7%2A0.+09
=0.+189