Question

An ordinary die has four blank faces. One face marked $2$, an other marked $3$. Then the probability of obtaining a total of exactly $12$ in $5$ throws is

• A. $\frac{15}{6^4}$
• B. $\frac{10}{6^4}$
• C. $\frac{5}{6^4}$
• D. $\frac{6}{6^4}$

Answer 1

The correct option is C $\frac{5}{6^4}$

Possible outcomes are 0,0,0,0,2,3

Probability of obtaining a total of exactly 1212 in 55 throws is

Favourable outcomes are

2,2,2,3,3 no. of ways =5!/(3!*2!)=10

0,3,3,3,3 no. of ways =5!/(4!*1!)=5

Probability of 2,2,2,3,3=10*($\frac{1}{6^5}$)=$\frac{10}{6^5}$

Probability of 0,3,3,3,3=5*($\frac{4}{6^5}$)=$\frac{20}{6^5}$

Total probability=$\frac{30}{6^5}$=$\frac{5}{6^4}$