Probability part two

The largest probability that you can have is 1. A probability of 1 means that something is certain to happen. Here is an example. If you pick a card at random from a standard deck of cards with four suits (spades, clubs, hearts and diamonds), what is the probability of picking a spade, club, heart or diamond? Well, this is certain to happen and the probability is 1.

We can write this more formally, in mathematical language. We can write the probability of picking a spade, club, heart or diamond as P(picking a spade, club, heart or diamond).

We know that 52 of the cards are spades, clubs, hearts or diamonds and that there are 52 cards. Therefore,

P(picking a spade, club, heart or diamond) $= \frac{52}{52} = 1$

The smallest probability you can have is zero. An example of this would be in a standard pack of playing cards with suits of spades, clubs, hearts and diamonds, what is the probability of picking out a loaf of bread. There are no loaves of bread in a standard pack of playing cards and so the probability is $\frac{0}{52} = 0$

Zero is the lowest probability. There is nothing less likely, there are no negative probabilities. One is the highest probability. There are no probabilities higher than one. At the halfway point between impossible and certain the probability is $\frac{1}{2}$ . At this point the event is as likely to happen as it is not to happen. This is called an even probability. An example of this using our playing cards is P(picking a club or a spade). Above a probability of $\frac{1}{2}$ an event is more likely to happen. Below a probability of $\frac{1}{2}$ an event is more likely not to happen.

Below is a simple probability scale ranging from zero to one.

Notice that an even probability of $\frac{1}{2}$ is shown as $0.5$ . Probabilities can be expressed as fractions, decimals, percentages or ratios. For an even chance this is $\frac{1}{2}$ , $0.5$ , $50%$ or $1:1$ .

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