Question

In a​ lottery, the top cash prize was ​$675 ​million, going to three lucky winners. Players pick four different numbers from 1 to 51 and one number from 1 to 41.
A player wins a minimum award of $ 150 by correctly matching three numbers drawn from the white balls​ (1 through 51​) and matching the number on the gold ball​ (1 through 41​). What is the probability of winning the minimum​ award?

Answer 1

You must match exactly 3 of the 4 white numbers and the gold ball. The probability is

P = [C(4,3)·C(47,1) / C(51,4)] · (1/41)
= 188 / (249,900·41)
= 47 / 2,561,475 ≈ 0.00001835.

So the chance is about 0.001835% (roughly 1 in 54,500).