There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is

Select one answerSingle correct

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Solution

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Official answer: D) 4/15

Quantitative Aptitude

Total number of socks = $3 + 4 + 3 = 10$ .

The total number of ways to choose 2 socks from 10 is:

\binom{10}{2} = \frac{10 \times 9}{2} = 45

The number of favorable outcomes where both socks are of the same color:

Both red: $\binom{3}{2} = 3$
Both green: $\binom{4}{2} = 6$
Both blue: $\binom{3}{2} = 3$

\text{Total favorable ways} = 3 + 6 + 3 = 12

Therefore, the required probability is:

P(\text{same colour}) = \frac{12}{45} = \frac{4}{15}

Hence, option (D) is correct.

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This Quantitative Aptitude previous year question is Q60 of the GATE CSE 2017 Set 2 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

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Quantitative Aptitude in GATE CSE

Quantitative Aptitude has 53 GATE CSE PYQs across 13 papers from 2011 to 2026. 26 of them are 1-mark MCQs like this one, and GATE CSE 2017 Set 2 has 3.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.