Probability Training
However what is certain is that a good understanding and feel for probability is a very important life skill. Many things in life, whether we think of them as probability or not, are just that.
For instance, if we are told there is a 1% chance that it will rain today, not many of us will take an umbrella. Perhaps without realising it, we are making a probability calculation.
If anyone likes to make the occasional bet, then probability comes directly into the equation. Toss a coin five times and get five heads, and ask people to state what is most likely to come next - the majority of people will say tails. This shows that probability can appear counter-intuitive, because in fact on any one toss you are just as likely to get a head as a tail, assuming no bias in the coin.
So, just what is probability? Well, it is defined as "a measure of how likely it is that some event will occur", and in turns out that it is at the core of how the universe works. Unlike the Newtonian mechanical vision of the universe, where everything was thought to be capable of prediction if you just knew enough about the preceding conditions, modern physics has shown that the world is inherently indeterministic through quantum mechanics.
Worked example
Let's work through a simple problem to work out how to approach a probability question.
What is the probability of rolling two dice and each coming up 6?
So, we need to calculate the chance of this happening. Now, we know that there are six possible options on a standard die (singular of dice). This means that if we roll one die, it could be 1,2,3,4,5,6.
Now let's convert that to a fractional chance score for each number. To do this, you need to know two very basic, key facts about probability. The first is that if something is impossible it has probability 0. The second is that, if something is certain, it has probability 1. If you ever get a probability of greater than 1 or less than 0, something has gone horribly wrong.
Now, if there are six possible options, then it stands to reason the chance of each is not 1/1, but rather 1/6. So there is 1/6 (which means 'one in six') chance of each combination. So that's one die sorted. And for two dice, we know that each one has a 1/6 chance of coming up '6'.
Now, since we know each die independently has a 1/6 chance, should we add them together? This would give us 1/6 + 1/6 which is 2/6 or 1/3. No! Intuitively we should know this is wrong because it says it is more probably for two dice to come up 6 than just rolling one! Based on this logic if we roll six dice we are guaranteed for all six to land on a six!!!
Rather, what we need to do is multiply them, giving us 1/6 x 1/6, which is 1/36 - that's one-in-thirty-six. And that is the probability, or chance, of rolling a six with two dice.
Hopefully this has given some useful insights into what probability it, why it is important, and how to reason your way through a simple probability question. Was this of use? Would you like to see more information and worked examples on probability? Just let us know through the contact form.
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