Question

A drawer contains 12 brown socks and 12 black socks, all unmatched. A man takes socks out at random in the dark. 21. Required information The least number of socks that he must take out to be sure that he has at least two black socks is _____.

Answer 1

6 socks

Explanation:

What we must do is calculate the probability of this happening, that he takes out two black socks in the first two taken out.

There are 12 black socks and in total they are 24, therefore the probability of drawing 1 is:

12/24

and now the probability of getting another one is 11 (there is one less outside) and in total they are 23:

11/23

the final probability is the multiplication of these events:

(12/24) * (11/23)

P = 0.24

Now, to know how many you should get, we multiply the probability by the total number of socks, that is:

0.24 * 24 = 5.76

So you must take out at least 6 socks for the above to happen.