Question

A pair of dice is thrown. The probability of getting a total of $10$ is:

• A. $\frac{2}{26}$
• B. $\frac{1}{4}$
• C. $\frac{1}{12}$
  
• D. $\frac{5}{36}$

Answer 1

The correct option is C $\frac{1}{12}$

Total no. of outcomes when two dice are thrown are:-

$(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)$

$(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)$

$(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)$

$(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)$

$(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)$

$(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)$

Hence, $n\left(S\right)=36$

Sum of $10$ in pair of die can be:

$(4,6),(5,5),(6,4)$

Outcome of sum of 10 is $n\left(E\right)=3$

$\therefore$ Probability of getting a total of 10 is $=\frac{3}{36}=\frac{1}{12}$