Maths Games For Kids - The Possibilities Of Probability (part 1 Of 3)

Probability, the mathematical study of chance or likelihood

, impinges on many aspects of our lives, from how well we perform at school to our health. However, it is uncommon for kids to be introduced to probability at school before Key Stage 3. The first reason for this omission is that probability is considered a difficult subject to teach to younger kids. This is a pity, as many Key Stage 2 pupils find probability an engaging subject and one which helps them consolidate their knowledge of other areas of mathematics, particularly arithmetic. The second reason is rather more sociological, in that some teachers perceive that the association between the study of probability and gambling makes it an unsuitable subject for study. There is, however, a strong counter argument which says that kids who have been introduced to probability at an early age are less likely to be drawn to gambling, as they will appreciate the extent to which the odds are stacked against the gambler.

Introducing Kids to Probability

Perhaps the most important and difficult principle to get across to kids is that probability deals with likelihood, rather than certainty. A practical way of introducing these concepts is the tossing of a coin. A coin when tossed may land on one or other of its two faces. The face which carries the depiction of the monarch is described as the head, while the other side is the tail. There is a very small chance that the coin could land and stay resting on its edge in an upright position. However, the likelihood of this is so remote that it can safely be ignored when talking to kids about probability. The possible outcomes of tossing a single coin is that it lands either as a head (H) or a tail (T). There is nothing about the design or aerodynamics of a coin which favours one result over the other, so the probability of getting a head is 1 in 2, also expressed as 0.5, and the probability of getting a tail is also 1 in 2 (0.5).

Practical Coin Tossing Exercise

Having explained the probability of getting a head or a tail when a coin is tossed, it's interesting to explore with the group what each thinks the outcome would be if a coin was tossed ten times in succession. Some kids will be adamant that the outcome will be 5 heads and 5 tails, whereas others will appreciate that any result ranging between all 10 throws resulting in a head and all 10 throws resulting in a tail is possible. Next ask each kid to toss a coin 10 times and record the results in terms of the total number of heads and tails. There will, indeed, be a range of results, but the tendency will be for the results to cluster towards the centre of the range with 4, 5 or 6 heads.

Objects Can't Remember

It is common for people, both kids and adults, to believe that if you have thrown 10 heads in a row, this will influence the likelihood of the next throw being a head. What is interesting is that some people will think it is more likely and others think it less likely. Those who are knowledgeable about probability will appreciate that if the coin is tossed often enough that the balance between heads and tails will tend towards equality, which steers them to thinking that this will favour a tail. However, those of a slightly superstitious, or perhaps even suspicious, nature will think that another head is more likely. One of the important rules of probability is that if you consider successively occurring events, the outcome of one event is not influenced by the outcome of preceding events. A coin cannot remember that it has been landed as a head 10 times in a row, so when you throw it an eleventh time the probability of a head remains 1 in 2.

In the next article we'll increase the complexity of the probability calculations by looking at a situation in which two coins are thrown simultaneously.

by: Hannah McCarthy

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