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) $^{n}$
$=1-\left(\frac{35}{36}\right)^{n}$