En red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their colour. The room is in pitch darkness and you want two matching socks. What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match?

We need to find out, the minimum number of socks to be taken out from the dark room so that there is at least a pair of matching socks comes out of the drawer.

Let us consider the cases:

First Two socks pulled out of the drawer.

Case 1: Both are red or both are blue.

In this case, the matching pair is ready.

But there can be other case as well.

Case 2:

One red and one blue color taken out.

Now, when we pull the third, there will be either red or blue.

That will make a pair.

Therefore, to cover up all the cases and to be certain to get a matching pair out of the drawer, at least 3 socks must be taken out.

So, the answer is:

We need to take out at least 3 socks.

MrRoyal MrRoyal · Answer 2 · 2021-12-02T12:03:44+01:00

The number of socks that determines a matching pair is an illustration of probabilities

The smallest number of socks is 3

The number of socks is given as:

[tex]\mathbf{Red = 10}[/tex]

[tex]\mathbf{Blue = 10}[/tex]

There are two colors of socks in the drawer

This is represented as:

[tex]\mathbf{n = 2}[/tex]

So, the smallest number of socks to determine matching pair is

[tex]\mathbf{Smallest = n + 1}[/tex]

Substitute 2 for n

[tex]\mathbf{Smallest = 2 + 1}[/tex]

Add

[tex]\mathbf{Smallest = 3}[/tex]

Hence, the smallest number of socks is 3