Question

A die has four blank faces and two faces marked $3$. The chance of getting a total of $12$ in $5$ throws is

• A. $^{5}{{C}_{4}}{{\left( \frac{1}{3} \right)}^{4}}\left( \frac{2}{3} \right)$
• B. $^{5}{{C}_{4}}\left( \frac{1}{3} \right){{\left( \frac{2}{3} \right)}^{4}}$
• C. $^{5}{{C}_{4}}{{\left( \frac{1}{6} \right)}^{5}}$
• D. $^{5}{{C}_{4}}{{\left( \frac{1}{6} \right)}^{4}}\left( \frac{5}{6} \right)$

Answer 1

Answer: (A)

$^{5}{{C}_{4}}{{\left( \frac{1}{3} \right)}^{4}}\left( \frac{2}{3} \right)$

Answer 2

Probability of success, $p=\frac{2}{6}=\frac{1}{3}$ and probability of failure, $q=\frac{2}{3}$
$\therefore$ Required probability ${{=}^{5}}{{C}_{4}}{{\left( \frac{1}{4} \right)}^{4}}\left( \frac{2}{3} \right)$