Question

A lottery is conducted in which 7 winning numbers are randomly selected from a total of 62 numbers (1-62). In addition, the Powerball, a single winning number, is selected from an independent pool of 26 numbers (1-26). You select 7 numbers from the pool of 62 numbers.

What is the probability that you selected none of the winning numbers?

Answer 1

You select 7 numbers from the pool of 62 numbers.

What is the probability that you selected none of the winning numbers?

no. of ways to select 7 numbers from 62 numbers = 62C7 = 62!/((7!)*(62-7)!) = 491796152

there are 7 winning numbers so if we want to select none of them

then we have to choose 7 numbers from the 55 (62-7) non winning numbers

no. of ways to select 7 numbers from 55 non winning numbers = 55C7 = 55!/((7!)*(55-7)!) = 202927725

P(you selected none of the wiining numbers)

= (no. of ways to select 7 numbers from 55 non winning numbers) / (no. of ways to select 7 numbers from 62 numbers)

= 202927725 / 491796152

P(you selected none of the wiining numbers) = 0.4126

P.S. (please upvote if you find the answer satisfactory)