GATE CS 2015 Set 1 Q.3 (GA Q.3): Quantitative Aptitude

Given Set $A = \{2, 3, 4, 5\}$ and Set $B = \{11, 12, 13, 14, 15\}$ , two numbers are randomly selected, one from each set. What is the probability that the sum of the two numbers equals $16$ ?

$0.20$

$0.25$

$0.30$

$0.33$

Official answer and solution

Official answer: A
From: Official GATE 2015 answer key

Solution

Count the number of pairs $(a, b) \in A \times B$ such that $a + b = 16$ .

The sets are $A = \{2, 3, 4, 5\}$ ( $|A| = 4$ ) and $B = \{11, 12, 13, 14, 15\}$ ( $|B| = 5$ ).

The total number of possible pairs selected equiprobably is:

|A \times B| = 4 \times 5 = 20.

We require $a + b = 16$ with $a \in A, b \in B$ :

If $a = 2$ , $b = 14 \in B$ .
If $a = 3$ , $b = 13 \in B$ .
If $a = 4$ , $b = 12 \in B$ .
If $a = 5$ , $b = 11 \in B$ .

There are exactly 4 favorable outcomes: $\{(2, 14), (3, 13), (4, 12), (5, 11)\}$ .

The probability is:

P = \frac{4}{20} = 0.20.

This matches option A.

Final answer

Common trap

Miscounting the size of set B as 4 instead of 5, which would erroneously give $4/16 = 0.25$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 1
Question: 3 of 65, printed as GA Q.3
Section: General Aptitude

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