Chapter 12, Problem 3CCSR

To determine

To find: the probability of getting odd on both cube if pair of cubes is rolled.

Answer to Problem 3CCSR

The option $\text{C}$ is correct option.

Explanation of Solution

Given:

The pair of cube or dice is thrown.

Concept used:

The probability the first die shows an odd is $\frac{1}{2}$ and similarly the second die shows an odd is $\frac{1}{2}$ .

Since, the dice fall independently, the probability will be multiplication of both the probability of two dice.

Mathematically:

  $\text{p}\left(\text{both are odd }\right)\text{=p}\left(\text{first is odd }\right)\text{×p}\left(\text{second is odd }\right)$ .

Calculation:

A cube has $\text{6}$ sides so there are $\text{6}$ choices $1,2,3,4,5\text{ and }6$ form where $3$ odd numbers $1,3,5$ .

For a single cube the probability of getting an odd is $\frac{3}{6}=\frac{1}{2}$ .

The probability for getting $\text{odd}$ for pair of cubes is $\left(\frac{1}{2}\right)\times \left(\frac{1}{2}\right)=\frac{1}{4}$ .

Hence, the option $\text{C}$ is correct option.