2008
Problem - 1626
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?
There are totally $3$ possibilities to choose one approving voter and two disapproving voters: $YNN$, $NYN$, and $NNY$. Each of these cases has the same probability to occur: $\frac{7}{10}\times\frac{3}{10}\times\frac{3}{10}$. Hence the answer is $$3\times\frac{7}{10}\times\frac{3}{10}\times\frac{3}{10}=\frac{189}{1000}$$