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)

$\frac{25}{216}$

Answer 2

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