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It's a Tie

Age 7 to 11 Challenge Level:

Jannis from Northcross Intermediate said:

"I think Kaia was right. The ties come out of the closet randomly. We know each tie has 1 eighth of a chance to be pulled out, so its quite likely that the father will not wear 1 tie twices in the week. But its random so there is a chance of him wearing a tie twice in the week."

Making the point that they're probabilities so you can't be sure.

Matthew and James from Stradbroke Primary did an experiment, and found that they picked the same tie twice in 9 out of 10 weeks. Ege and Onur from FMV Ozel Erenkoy Isik Primary School, Turkey, also did experiments, and you can find their results here and here .

Some people have tried to calculate the probability of picking the same tie twice, but none correctly yet. Here is what happened when we tried the experiment:

We found that there were:
6 weeks out of 20 when he wore a different tie every day (green), so the probability of this is 6/20,
12 weeks out of 20 when he wore the same tie twice in a week (blue), so the probability is 12/20, and
2 weeks out of 20 when he wore the same tie more than twice, so the probability of this is 2/20.

These are only approximate probabilities, and each time you do the experiment you will get a different answer. You can improve the approximation by increasing the number of times you do the experiment and adding up all the results as this will be more accurate.

Here are some some photos of children working on this problem:

preparing materials
Preparing materials
drawing ties
Drawing ties
completing a table
Completing the table
collating results
Collating results