Question

Two dice are thrown together $4$ times. The probability that both dice will show same numbers twice is -

• A. $\frac{1}{3}$
• B. $\frac{25}{36}$
• C. $\frac{25}{216}$
• D. None of these

Answer 1

Answer: (C)

The probability of showing same number by both dice $p = \frac{6}{36} = \frac{1}{6} $
In binomial distribution here $n = 4, r = 2, p = \frac{1}{6}, q = \frac{5}{6} $
$\therefore $ req. probability = $^nC_r \; q^{n -r} p^{r} = {^4C_2} \left(\frac{5}{6}\right)^{2} \left(\frac{1}{6}\right)^{2} $
$ = 6 \left(\frac{25}{ 36}\right) \left(\frac{1}{36}\right) = \frac{25}{216} $