Question

A pair of dice are thrown, if 5 appears on atleast one of the dice, then the probability that the sum is 10 or greater, is

• A. $\frac{11}{36}$
• B. $\frac{2}{9}$
• C. $\frac{3}{11}$
• D. $\frac{1}{12}$

Answer 1

The correct option is C $\frac{3}{11}$

Sample space is $(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(1,5)(2,5),(3,5),(4,5),(6,5)$

$n\left(S\right)=11$

Let A be the event that the sum is 10 or greater.

A = $(5,5)(5,6)(6,5)$

$n\left(A\right)=3$

$\therefore$ P(A) = $\frac{n\left(A\right)}{n\left(S\right)}$

$=\frac{3}{11}$