Question

Two dice are thrown $n$ times in succession. The probability of obtaining a double six at least once is

• A. ${\left(\frac{1}{36}\right)}^n$
• B. $1-{\left(\frac{35}{36}\right)}^n$
• C. ${\left(\frac{1}{12}\right)}^n$
• D. None of these

Answer 1

Answer: (B)

If $p$ is the probability of success and $q$ is the probability of failure, then the probability of at least one success in $n$ trial is $1-q^n.$
Here, $p=$ Probability of getting double six in two dice
$=\frac{1}{6^2}=\frac{1}{36}$ and $q=\frac{35}{36}$
$\therefore$ Required probability $=1-$ (Probability of not getting double six) ${}^n$
$=1-{\left(\frac{35}{36}\right)}^n$