Cool Math 4 Kids: Fun with Probability

Pretend it is dark.

English: Socks on feet.

Socks on feet. (Photo credit: Wikipedia)

You have to find a pair of socks in your drawer that match.

How many socks do you have to take out of your drawer to be sure you get a pair?

Materials:

  • Paper bag
  • 4 pairs of matching socks of different colors, like white, black, red, brown. You could also use pairs of buttons or pairs of jelly-beans the same color

Instructions:

  • Put two pairs of the socks in the paper bag.
  • Ask your grandchild how many socks they have to take out of the bag to be sure they get a pair.
  • To illustrate what is happening, take the four socks out of the bag. Ask your grandchild to pick up one sock of each color. Then, ask them how many more socks they need to pick up to make a pair.

What Should Happen?

The answer is three.

Repeat with three pairs, then four pairs of socks.

Each time, put them in the bag first and ask how many they need to draw out.

Then, lay them all out in the open, have them pick up one of each color and ask how many more they need to pick up to get a pair.

The answer will always be half of the socks, plus one.

That is, they might get a pair with the first two or three socks, but, to be sure they get a pair, they have to pick out half the socks, then one more.

This is true no matter how many pairs of socks of different colors they use.

Optional: Equation

You can represent the physical reality we have just demonstrated with an equation.

X represents the number of socks you have to take out of the bag to be sure you get a pair.

N represents the number of socks in the bag.

We assume there is a pair of each color of socks.

We assume there is the same number of socks of each color, that is, 2 black, 2 red, 2 white.

To find the number of socks you need (X), you divide the number of socks (N) in half and add 1.

X = N/2 +1

For example:

If you put four socks in the bag, two black and two white:

N = 4 (the number of socks in the bag)

X = 4/2 + 1

X= 4 divided by 2 = 2

X = 2 + 1 = 3

X = 3

You have to take 3 socks out of the bag to be sure you get a pair.

Thanks to Resources for Educators, Math+Science Connection, for this activity. www.rfeonline.com

 

Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers

http://newgrandmas.com

 

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