AMC10 2008 10B, Problem 17

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?

Solution: Letting Y stand for a voter who approved of the work, and N stand for a person who didn't approve of the work, the pollster could select responses in $3$ different ways: $\text{YNN, NYN, and NNY}$. The probability of each of these is $(0.7)(0.3)^2=0.063$. Thus, the answer is $3\cdot0.063=\fbox{{{{0.189}}}}$

Answer: {{{0.189}}}