Question

When two dice are thrown $n$ number of times, the probability of getting a doublet at least once is greater than $80\%$ and the least value of $n$ is $\lambda$ , then the value of $\lambda$ is equal to

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

Answer: (D)

Probability of getting a doublet $=\frac{6}{36}=\frac{1}{6}=p$ (Let)
Let, $q=1-p=\frac{5}{6}$
Probability of not getting doublet, using Binomial Probability Distribution $={}^n{C}_0^{}{p}^0{q}^n={\left(\frac{5}{6}\right)}^n$
Probability of getting a doublet at least once $>\frac{4}{5}$
$1-{\left(\frac{5}{6}\right)}^n>\frac{4}{5}$
$\Rightarrow {\left(\frac{5}{6}\right)}^n<\frac{1}{5}$
$\Rightarrow n\ge 9$