Question

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.

Answer 1

The probability of getting a six in a throw of die 1/6 and not getting a six is 5/6.

Let `p = 1/6 and q = 5/6`

The probability that the 2 sixes come in the first five throws of the die is `""^5C_2 (1/6)^2(5/6)^3 = (10xx(5)^3)/(6)^5 `

∴ Probability that third six comes in the sixth throw  `(10xx(5)^3)/(6)^5 xx 1/6`