Question

How many times should you need to throw a dice in order to have a probability of 99% or higher of rolling a six at least once?

Answer 1

P(rolling a six on a die) = 1/6

P(not rolling a six) = 1 - 1/6 = 5/6

Let n be the number of times you need to throw a dice in order to have a probability of 99% or higher of rolling a six at least once

P(rolling a 6 at least once on n rolls) = 1 - P(all rolls are not six)

0.99 = 1 - (5/6)ⁿ

(5/6)ⁿ = 0.01

n log (5/6) = log 0.01

n = log 0.01 / log (5/6)

n = 25.3

26

You need to throw a dice 26 times in order to have a probability of 99% or higher of rolling a six at least once