Question

Suppose you are asked to pick 3 numbers from 1 to 20 to win a prize. What is the probability that one of the numbers you will pick is the winning number?

Answer 1

Another way to calculate it is:

P(1st pick is not the winner) = 19/20 because 1 out of 20 is winner
P(2nd pick is not the winner) = 18/19 because only 19 numbers left
P(3rd pick is not the winner) = 17/18

P(not picking the winner) = P(1 no win) * P(2 no win) * P(3 no win)
=19/20 * 18/19 * 17/18 = 17/20

P(picking winner) = 1 - P(no win) = 1 -17/20
= 3/20 = 0.15

Answer 2

Each number has a 1/20 chance of being the winner.
You pick 3 numbers, so you have three times the chance of having the winning number.

3 * 1/20 = 3/20 = 0.15

The probability you have the winning number is 0.15.