Question

A pair of dice is thrown. The probability of getting a total of $8$ or $10$ is.......

• A. $\frac{2}{25}$
• B. $\frac{2}{9}$
• C. $\frac{1}{3}$
• D. $\frac{27}{128}$

Answer 1

The correct option is B $\frac{2}{9}$

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 8 in pair of die can be:

$\left\{\right(2,6),(3,5),(4,4),(5,3),(6,2\left)\right\}$

Outcome of sum of $8$ is $5$

Sum of 10 in pair of die can be:

$\left\{\right(4,6),(5,5),(6,4\left)\right\}$

Outcome of sum of $10$ is $3$

$\therefore$ Probability of getting a total of $8$ is $=\frac{5+3}{36}=\frac{8}{36}=\frac{2}{9}$