Question

A pair of dice is thrown, it $5$ appears on at least one of the dice, then the probability that the sum is $10$or greater is

• A. $11/36$
• B. $2/9$
• C. $3/11$
• D. $1/12$

Answer 1

The correct option is D

$1/12$

Explanation for the correct option:

Calculate the probability.

If two dice are thrown, the total number of cases $=36$

Let $A$be the event that at least one of the dice shows $5$.

$A=\left\{\right(1,5,),(2,5),(3,5),(4,5),(5,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6\left)\right\}$

And let $B$be the event that the sum is $10$ or greater than $10$.

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

$A\cap B=\left\{\right(5,6),(6,5),(6,6\left)\right\}$

Required probability

$$\begin{gathered} =\frac{(A\cap B)}{Totalcases} \\ =\frac{3}{36} \\ =\frac{1}{12} \end{gathered}$$

Hence, the correct option is D.