Question

One of your friends likes buying scratch off lottery tickets. One day, upon reading in the fine print that the probability that any given ticket is a winner is one in a thousand, he wistfully wishes aloud that he could afford one thousand tickets so that he could be sure to win.

How many tickets would he have to buy to have a 90% chance of winning?

Answer 1

Let the number of tickets to be bought be n to be 90% sure to have a 90% chance of winning.

Therefore, we have here:

Probability that none of the n tickets are winner <= 0.1

(1 - 0.001)ⁿ <= 0.1

0.999ⁿ <= 0.1

Taking natural log both sides, we get here:

nLn(0.999) <= Ln(0.1)

n >= 2301.43

Therefore 2302 is the minimum number of tickets that are to be bought to be 90% sure of winning.