**Problem**

Six coins are tossed
to decide a result for either “C” or “S”.
Assuming that the coins are
fair,
and that the results of the tosses are independent,
calculate the probability that all the tosses are in favour of “C”. |

**Introduction**

**Hot in recent news is the story of the purported six coin tosses that were needed to determine certain county delegates in the race between Hillary Clinton and Bernie Sandersin the state of Iowa. All six coin tosses were in favour of Hillary Clinton, and the result is so improbable that some people said it was “hillarious”.**

How is the probability calculated? This is an example of mathematics in real life events that has the potential to affect the

**Solution**

**Discussion**

In order to make the calculation, we make
two assumptions:

(1) that the coins were

*fair*, and
(2) that the coin toss results are

So, what does it mean that the coins are “fair”? It means that the probability of getting a “heads” is the same as the probability of getting a “tails”, which means ½ for each.

Coin toss results can be “heads” or “tails”. These are examples of

*independent*.So, what does it mean that the coins are “fair”? It means that the probability of getting a “heads” is the same as the probability of getting a “tails”, which means ½ for each.

Coin toss results can be “heads” or “tails”. These are examples of

*events*. An event is something that can happen or not happen, and we associate a*probability*with it. The probability is a number that indicates how likely the event happens. It is between 0 and 1 inclusive. Zero probability means a practically impossible event. A probability of 1 means a practically certain event. [The reason for me using the word “practically” is technical, which I shall not discuss.] If the events do not affect one another (i.e. in our case, the coin tosses are not affected by the other coin tosses) then the events are said to be*independent*. If the events are independent, then we can simply multiply the individual probabilites together, as above. If the events are dependent, the calculation would be more complicated.
So are the coin toss results valid? I do not know. All I can say is:

*improbable*does not mean*impossible*. Mathematics cannot tell whether the above assumptions (1) and (2) are correct. But at least I “lay all the cards on the table”, so that astute students of probability know the*basis*of these calculations. It is up to you to decide, but at least you would have made a mathematically-informed decision. There could be other twists to the story, which is beyond the scope of this article. This is one of the reasons why you need to learn mathematics carefully and think critically, whether or not you would become a mathematician,engineer, teacher or have a mathematics-intensive career.
H08. Make suppositions

H10. Simplify the problem

H11. Solve part of the problem

**Suitable Levels**

*****GCE ‘O’ Level “Elementary” Mathematics (Number patterns, with algebra)

* other syllabuses that involve probability

* anybody in the whole wide world!
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