A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.

Explanation

The probability of getting a six in a throw of die `1 / 6` and not getting a six is `5 / 6`.
Let `p=frac{1}{6} and q=frac{5}{6}`

The probability that the `2` sixes come in the first five throws of the die is `=^5 C_{2}(frac{1}{6})^{2}(frac{5}{6})^{3}=frac{10 times(5)^{3}}{(6)^{5}}`

`therefore` Probability that third six comes in the sixth throw `frac{10 times(5)^{3}}{(6)^{5}} times frac{1}{6}`


`=frac{10 times 125}{(6)^{6}} `

`=frac{10 times 125}{46656} `

`=frac{625}{23328}`