50 people are entered in a weekly drawing where one winner is chosen each week for 17 weeks.

Question

The winning names are put back in each week, so there is a full 50 people each week. What are the odds of winning 3 times out of the 17 weeks? 

Answer 1

Binomial Distribution (17 Bernoulli trials) with prob. of success = 1/50 = 0.02, q = prob. of failure 0.98;

P(exactly 3 wins in 17 trials) = 17C3 p³q¹⁴ = (680)(0.02³)(0.98¹⁴) = 4.0998 × 10^-3 or 

0.0041