Sock-ability

Probability Level 3

I have 7 pairs of red socks, 6 pairs of blue socks, and 5 pairs of green socks in my drawer. If I randomly pick out 4 socks, what is the probability that I will get (at least) a matching pair?

Details and Assumptions:

Besides the color, there is no difference between a left sock and a right sock.

0

\frac{1}{4}

\frac{1}{3}

\frac{1}{2}

\frac{2}{3}

\frac{3}{4}

1

1 solution

Discussions for this problem are now closed

Chung Kevin
Jan 27, 2015

Note that there are only 3 different colors of socks. Hence, when you pick out 4 socks, you are guaranteed to have 2 socks that are of the same color, which will form the matching pair.

Hence, the probability is 1.

Well, what if a matching pair includes a left sock and right sock? @Calvin Lin , I'm not sure about that. I answered $\frac {2}{3}$ as a result.

Sharky Kesa - 6 years, 4 months ago

Well i also dohav d same doubt an i also answered d same..

chinmoy dutta - 6 years, 4 months ago

That's a valid concern. Let me add that condition in.

@Sharky Kesa Can you show how you arrived at $\frac{2}{3}$ as the answer in this case?

Calvin Lin Staff - 6 years, 4 months ago

@Calvin Lin – 4 socks can be of same color also

Pavan Kumar Bharti - 6 years, 4 months ago

Uhm, the question asked for a matching pair. That's matching pairs (2), so yeah, it's still a valid case.

Joeie Christian Santana - 6 years, 4 months ago

4 socks can be of same color also

Pavan Kumar Bharti - 6 years, 4 months ago

instead of one pair it is better to use 'atleast' one pair.

It was a nice one @Chung Kevin . :-)

Bhargav Upadhyay - 6 years, 4 months ago

Sock-ability

1 solution

Discussions for this problem are now closed

0 pending reports