Question

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

• A. $\frac{{}^8{C}_3{.5}^5}{6^8}$
• B. $\frac{{}^7{C}_2.5^5}{6^8}$
• C. $\frac{{}^7{C}_2.5^5}{6^7}$
• D. $\frac{{}^7{C}_2.5^6}{6^7}$

Answer 1

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

Third six occurs on $8^{th}$ trial. It means that in first 7 trials we must get exactly 2 sixes and $8^{th}$ trial must result in a 6.
$\therefore$ Required probability $={}^7{C}_2\times {\left(\frac{1}{6}\right)}^2\times {\left(\frac{5}{6}\right)}^5\times \left(\frac{1}{6}\right)=\frac{{}^7{C}_2.5^5}{6^8}$