If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is:

$\frac{1}{2}$

The correct answer is Option (4) → $\frac{1}{2}$ ##

$A = \text{Sum of numbers obtained on throwing a pair of dice is } 9 = \{(3,6), (4,5), (5,4), (6,3)\}$

$A \cap B = \text{Number obtained on one of the die is 4 }$

$\text{ Sum of number obtained on the pair of dice is } 9 = \{(4,5), (5,4)\}$

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{2/36}{4/36} = 1/2$