One die to be rolled once

Probability Level 1

If we roll one die, what is the expected number of dice throws before we get the first 6?

Note: the roll of the 6 is included in the "number of throws before we get the first 6."

2 solutions

Ela Marinić-Kragić
Aug 9, 2015

For every number from 1 to 6 probability to get it in one throw is 1/6, so we expect 6 throws to get number!

$1\cdot \frac16+2\cdot \frac16(\frac56)+3\cdot\frac16(\frac56)^2+\dots+n\cdot\frac16(\frac56)^{n-1}+ \dots =$

$\frac16 \left[1+2(\frac56)+\dots+n(\frac56)^{n-1}+\dots\right]=\frac16\cdot \frac1{(1-\frac56)^2}=6$

How is there a 5/6?

Ship Boat - 3 years ago

It's the chances of not getting a 6. How many numbers except 6? 5... therefore $\frac{5}{6}$

Akshay Krishna - 2 years, 5 months ago

Siddhartha Bhattacharya
Jan 4, 2021

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