How to get heads from ten consecutive coin tosses

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

27 December 2020

Do you think you can toss a coin ten times and get consecutive heads through out? It sounds impossible, doesn’t it? You would need to be very lucky, wouldn’t you? Perhaps, “One-in-a-million”.

Well, it turns out that the chances of getting ten consecutive heads are not as rare as many might think. If you toss a coin once, the chances are 50:50, that is it could go either way.

Thus, if ten people were given one similar coin each and then asked to toss them, the outcome will be about five will get heads and the rest tails. What if the group was larger, say 1,000?

Again, because of the 50:50 chances, about 500 will get heads and 500 tails. Now, suppose all those who got tails are requested to leave so that only 500 who tossed heads are left behind.

If these 500 are asked to repeat the toss, about half (250) will get heads again and the others, tails. As before, those with tails are told to leave and the process repeated. The numbers left in play after each round will be approximately, 125, then 62, 31, 16, 8, 4, 2 and finally, one person is left.

In total, there ten rounds and, each time, only those who get heads are left in in play So, the last person must have been the lucky fellow who got ten consecutive heads! Since the experiment started with 1,000 people, we can conclude that the chances of getting ten consecutive heads is about one in a thousand. It doesn’t sound so rare, after all.

But it might be argued that, when the numbers are small, that is, few people remaining, there is a good chance that all might toss and get tails. The chances of such an eventuality are easy to work out.

When there are only two people remaining, the possible outcomes are: H-H; H-T; T-H and T-T. These are four possibilities, out of which only one has both tails. Thus, the chance of this outcome is one in four.

By similar argument, when there are 4 people, the chances that no one will get heads are even lower: one in 16. And so on. Thus, to improve the likelihood of having some one making 10 coin tosses and getting heads all the time, it may be prudent to increase the size of the starting group, to say, 4,000. Still not so rare.