Question

A fair 10 sided die rolled until a 7 is first seen. What is the probability of rolling the die six times?

Answer 1

The probability of rolling a dice six time until a 7 is first seen is 0.059

Explanation:

The probability of getting a seven is equal to
`(1)/(10)`

The dice need to be rolled only six times.

This means that for the first 5 times the dice showed values other than 7 and in the last roll it displays 7

Hence the probability of rolling a dice six time until a 7 is first seen is

`((9)/(10))^5 * ((1)/(10))^1`

`= (9^5)/(10^6) \\= 5.90` % or 0.059