GATE 2017 EE (EE2) – Question 5

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

There are 3 red, 4 green and 3 blue socks. Two socks are chosen randomly. The probability that their colours match is

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

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Show answer and explanation

Correct answer: (D) $4/15$

Explanation

There are $\binom{10}{2}=45$ equally likely unordered pairs. Matching pairs consist of two red, two green or two blue socks, with counts 3,6,3 respectively.

The favourable total is 12, so probability is 12/45=**4/15, D**. The colours have unequal counts, so assuming one-third probability would be incorrect.

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