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A teacher wants a coin-tossing simulation in which the share of heads lands within 0.025 of 0.5 in…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A teacher wants a coin-tossing simulation in which the share of heads lands within $0.025$ of $0.5$ in about $95$ runs out of $100$ . How many tosses are needed? A drawing pin lands point up with a probability of about $0.6$ . How many drops make the band for the pin $0.04$ wide on each side?

Need a reminder? The key ideaShow

In about $95$ runs out of $100$ , the share of successes in $n$ tries lands within $2\sqrt{p(1-p)/n}$ of the probability $p$ . For a fair coin this is $\dfrac{1}{\sqrt{n}}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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