GATE CS 2015 Set 1 QGA-3 — General Aptitude

To find the probability that the sum of the two selected numbers is $16$, we determine the total number of outcomes and the number of favorable outcomes.

1. Total Outcomes:
We select one number from Set $A = \{2, 3, 4, 5\}$ (size $4$) and one from Set $B = \{11, 12, 13, 14, 15\}$ (size $5$).
$$\text{Total outcomes} = |A| \times |B| = 4 \times 5 = 20$$

2. Favorable Outcomes:
We look for pairs $(a, b)$ with $a \in A$ and $b \in B$ such that $a + b = 16$:

• If $a = 2$, then $b = 14$ (valid, since $14 \in B$)
• If $a = 3$, then $b = 13$ (valid, since $13 \in B$)
• If $a = 4$, then $b = 12$ (valid, since $12 \in B$)
• If $a = 5$, then $b = 11$ (valid, since $11 \in B$)

3. Probability:
$$\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{4}{20} = 0.20$$