Question

A person throws two dice, one the common cube, and the other a regular tetrahedron, the number on the lowest face being taken in the case of tetrahedron. The probability that the sum of the numbers appearing on the dice is $6$, will be

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. None of these

Answer 1

The correct option is C

$\frac{1}{6}$

Explanation for the correct option:

Step 1: Find the number of cases when the sum is $6$:

Given: A tetrahedron and a regular cube.

So, possible cases of (tetrahedron cube, common cube)$=(1,5),(2,4),(3,3)(4,2)$

Hence, $n\left(E\right)=4$

Step 2: Find the total number of cases for tetrahedron and regular cube:

The total number of possible cases will be the product of the total outcomes of both cases.

$\begin{array}{rcl}n\left(s\right)& =& 6\times 4\\ & =& 24\end{array}$

Step 3: Find the probability of the sum as $6$:

Divide possible cases by the total number of cases to get the probability.

Probability, $\begin{array}{rcl}p& =& \frac{4}{24}\\ & =& \frac{1}{6}\end{array}$

Hence, option (C) is the correct answer.