Gambling

Maths can be applied to things more interesting than you think.

In fact it is said that the whole area of Probability was invented primarily in an attempt to improve the chances of mathematicians betting on Roulette and card games in gambling halls some years ago.

The National Lottery sparked a new interest in probability as people were keen to find out what their chances of winning "The Big One" really were.

 

Probability lies within the "grey area" between total certainty (e.g. you will get older as each day passes) and total impossibility (e.g. pigs can't fly).

A simple scale has been developed to represent probability where:

0 = Impossible 1 = Certain

Probabilities have to be represented by decimal numbers between 0 and 1 (e.g. 0.25, 0.666, 0.5 etc.) or by fractions (e.g. etc.).

There's nothing complicated about probability it's really just "educated" guesswork. Rolling a dice when playing a board game is a good example of how probability can be used:

What's the chance (probability) of you throwing a 6?

Well, there are six sides on a dice, and you can only "throw" one of those sides i.e. you can throw a 1, 2, 3, 4, 5 or 6.

In other words there are 6 possible outcomes from throwing a dice (note that some people call one dice a die). Only one of those outcomes can be a 6, hence we say that the probability of throwing a 6 is (this can also be shown in its decimal form as 0.16666….). So in theory, if you roll a dice 6 times then on one of those rolls, you will be expected to get a 6. Remember that this is only a "best guess" in reality you may find that you roll the dice 6 times and are unlucky enough to get 1, 1, 1, 1, 1, 1! If we could predict the future we wouldn't need to worry about probability, however in the real world it is very useful for having a good shot at making accurate predictions.

Probability can be used to make all sorts of predictions. e.g. how likely it is that someone will pass their driving test after failing the first time, how likely it is that a poker player will get a running flush, how likely it is that we will have rain tomorrow, how likely it is that you will win the lottery on Saturday, how likely it is that motorists breaking the speed limit will have an accident etc.

 

If you chose a playing card at random from a pack of 52 cards, what is the probability that the card is an ace?

You need to know that a pack of playing cards has 4 aces, hence the probability is it makes further calculations easier to simplify this fraction, this gives us (i.e. 4 goes into 4 once and into 52, 13 times).

There are two rules to remember when working out more complicated probabilities:

RULE 1

To find the probability that one event OR another happens you ADD the probabilities.

For example: If two cards are chosen at random with replacement (i.e. after the first card is chosen it's put back in the pack). What is the probability that each card will be a King OR a Queen?

You need to know that there are 4 Kings and 4 Queens in a pack of cards.

The probability of each card being a King or a Queen is the probability of getting a King plus the probability of getting a Queen.

This can be written as:

P(King or Queen) = P(King) + P(Queen)

P(King or Queen) =

Then add the fractions together and simplify =

If one event OR another event can happen they are sometimes called mutually exclusive events.

 

RULE 2

To find the probability that one event AND another happens you MULTIPLY the probabilities.

For example: If two cards are chosen at random without replacement (i.e. after the first card is taken it is not put back in the pack - this leaves only 51 cards in the pack when the second card is taken). What is the probability that the two cards will be a King and a Queen?

 

P(King and Queen) = P(King) x P(Queen)

P(King and Queen) =

This means that if you take a card at random from a pack of cards, don't put it back and then take another, you will only pick both a King and a Queen 1 in every 165.75 times.

If one event AND another event can happen they are sometimes called independent events.

 

Note: You may have noticed when working out probabilities that they are slightly different to other topics in GCSE maths. For those of you who are addicted to formulas, there are no "miracle" formulas which can be used to work out all probabilities - you need to actually THINK about the problem, try to imagine what is happening and what the chances of events will be. The two rules already given will help a lot, and TREE DIAGRAMS will help you even more.