Question

Suppose that a certain precinct contains 350 voters, ofwhich 250 are democrats and 100 are republicans. if 30voters are chosen at random from the precinct, what is theprobability that exactly 18 democrats will be selected?

Answer 1

The probability that exactly 18 democrats will be selected will be 0.05793...

Explanation

Total number of voters in the precinct = 350

Democrats = 250 and Republicans = 100

Total number of ways for choosing 30 voters at random from the precinct will be : $^3^5^0C_{30}$

For selecting exactly 18 democrats , we need to select remaining (30-18) or 12 voters from 100 republicans.

So, the number of ways for selecting 18 democrats and 12 republicans will be :  $^2^5^0C_{18}*^1^0^0C_{12}$

Thus the probability $= \frac{^2^5^0C_{18}*^1^0^0C_{12}}{^3^5^0C_{30}}= 0.05793...$