Question

A die numbered 1 to 6 on its faces is rolled.
Statement 1: The probability that the number on the top will be a factor of 36 is $\frac{20}{24}$.
Statement 2: The probability that the number on the top will be more than 5 is $\frac{2}{12}$.

• A. Both statement 1 and statement 2 are true.
• B. Statement 1 is true, while statement 2 is false.
• C. Statement 1 is false, while statement 2 is true.
• D. Both statement 1 and statement 2 are false.

Answer 1

The correct option is A Both statement 1 and statement 2 are true.

(i) Out of the integers from 1 to 6, the factors of 36 are 1, 2, 3, 4, 6.
Hence, the required probability
$=\frac{\text{Number of factors of 36 below 7}}{\text{Number of integers from 1 to 6}}=\frac{5}{6}=\frac{20}{24}$.
Thus, statement 1 is true.
(ii) Out of the integers from 1 to 6, the only integer greater than 5 is 6.
Hence, the required probability
$\frac{\text{Number of factors of 36 below 7}}{\text{Number of integers from 1 to 6}}=\frac{5}{6}=\frac{20}{24}$.

Thus, statement 1 is true.

(ii) Out of the integers from 1 to 6, the only integer greater than 5 is 6.
Hence, the required probability
$=\frac{\text{Number of integers less than 7 but greater than 5}}{\text{Number of integers from 1 to 6}}=\frac{1}{6}=\frac{2}{12}$.
Thus, statement 2 is true.