Question

a die is thrown again and again until 3 sixes are obtained.Find the probability of obtaining the third six in the sixth throw of the die

Answer 1

Answer:

= 625 / 3 × 6⁵

Step-by-step explanation:

If there is third 6 in 6th throw, then five earlier throws should result in two 6's.

Hence, taking n = 5 , p $= \frac{1}{6}$ , $q = \frac{5}{6}$

      ∴ P(2 sixes) = P (5 , 2) = ⁵C₂p²q³

    P(2 sixes) = $\frac{5!}{2!3!}$ $(\frac{1}{6} )^{2}$ $(\frac{5}{6} )^{2}$

         = 10 × 125 / (6)⁵

∴        P(3 sixes in 6 throws ) = 10 × 125 / (6)⁵  × 1/6

                = 1250 / (6)⁶

                = 625 / 3 × 6⁵

Good luck !!