Question

A fair die is tossed eight times. Probability that on the eighth throw a third six is observed is

• A. ${}^8{C}_3\frac{5^8}{6^8}$
• B. ${}^7{C}_2\frac{5^5}{6^8}$
• C. ${}^7{C}_2\frac{5^5}{6^7}$
• D. None of these

Answer 1

The correct option is B ${}^7{C}_2\frac{5^5}{6^8}$

on the eight throw third six must appear, which implies that on first seven throws there must be two six.

probability of getting $6$ is $1/6$ and probability of not getting $6$ is $5/6$.

we must get two six in seven throws,

so the probability is ${}^7{C}_2{\left(1/6\right)}^2{\left(5/6\right)}^5$.

now prob that the eight throw is six is $1/6$.

so the final required probability is ${}^7{C}_2{\left(1/6\right)}^2{\left(5/6\right)}^{5}1/6$.