GATE CS 2017 Set 2 Q.60 (GA Q.5): Quantitative Aptitude

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

1/5

7/30

1/4

4/15

Official answer and solution

Official answer: D
From: Official GATE 2017 answer key

Solution

Calculate the total number of ways to choose 2 socks out of 10 and the number of ways to choose 2 socks of identical colour.

Total number of socks is $3 \text{ (red)} + 4 \text{ (green)} + 3 \text{ (blue)} = 10$ socks.
The total number of ways to pick any 2 socks without replacement is:

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

Count the favorable outcomes where both selected socks have the same colour:

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

Total favorable outcomes:

3 + 6 + 3 = 12

Therefore, the probability is:

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

This matches option D.

Final answer

Common trap

Computing probability with replacement ( $3/10 \times 3/10 + \dots$ ) instead of without replacement.

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

Source

Paper: GATE 2017 Computer Science and Information Technology (CS) Session 2
Question: 60 of 65, printed as GA Q.5
Section: General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source