GATE 2017 CS (CS2) – Question 5

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 1 mark · Multiple choice

There are 3 red socks, 4 green socks and 3 blue socks. Choose two socks uniformly without replacement. What is the probability they have the same colour?

$1/5$
$7/30$
$1/4$
$4/15$

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Correct answer: (D) $4/15$

Explanation

There are $\binom{10}2=45$ unordered pairs. Same-colour pairs number $\binom32+\binom42+\binom32=3+6+3=12$. Their probability is 12/45=4/15, D.

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