Question

Two dice are thrown together.

The probability that at least one will show its digit $6$ is

• A. $\frac{11}{36}$
• B. $\frac{36}{11}$
• C. $\frac{5}{11}$
• D. $\frac{1}{6}$

Answer 1

The correct option is A

$\frac{11}{36}$

Explanation for the correct option:

If two dice are thrown, the total number of sample space $=6^2=36$

The probability of getting at least $6=1-$ the probability of not getting $6$

The probability of getting $6=\frac{1}{6}$

Therefore, the probability of not getting $6$ on dice $1=\frac{5}{6}$

The probability of not getting $6$ on dice $2=\frac{5}{6}$

The digit $6$ will not show in both the dice $=\left(\frac{5}{6}\right)\left(\frac{5}{6}\right)=\frac{25}{36}$

Hence, The probability of getting at least $6=1-$ the probability of not getting $6$

$$\begin{gathered} =1-\left(\frac{25}{36}\right) \\ =\frac{36-25}{26} \\ =\frac{11}{36} \end{gathered}$$

Hence the correct option is option(A) i.e. $\frac{11}{36}.$