Are you smarter than a politician?

We all like feeling smarter than other people. Especially when those people are politicians.

With the general election coming up, we want to cover some maths mistakes made by politicians all the time. Can you succeed where they failed?

A few years ago, several MPs were given a maths quiz. More than half of them couldn’t answer the following question:

If I toss two coins, what is the probability of heads coming up both times?

If you know the answer, scroll to the bottom and leave a comment below! If you want to see how we’d work it out, read on…

Working:
Assuming the coins are unbiased, any one flip is equally likely to show heads or tails.
So if we flip one coin, there is a 50% (or 1-in-2) chance that it shows heads. If we flip another coin afterwards, then there is another 50% chance it lands heads-up. Since there is a 1-in-2 chance the first coin shows heads, and another 1-in-2 chance the second coin shows heads, the chances that both coins show heads is one-half times one-half, or 1-in-4.

We can see this illustrated in the picture below.

The first fork corresponds to flipping the first coin. We get heads with probability one-half. Then we flip the second coin. To get heads again we travel along the top line, again with probability one-half. We multiply these probabilities together to obtain one quarter.

Now it seems simple.
But if you can answer this question, you know probability better than 60% of surveyed MPs! Quite worrying, as the job of an MP is to weigh up the likelihood of different policy scenarios…

If you or your child want to get better at questions like these, Ned and Tom offer private maths tutoring. They teach maths which is useful in real-life, not just exams.

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