🎲 Probability: Chance in Numbers

What number will you get when you roll a die? Which colour will the spinner stop on? Things that look like pure luck can be described with numbers. This is called probability. Let’s look at it together!

There are 6 marbles in the bag: 3 red, 2 blue and 1 green. We will pick one without looking. Each marble is a different chance. So there are 6 possible outcomes. We count the marbles, not the colours.

We want to pick a blue marble. The number of wanted outcomes is 2, because there are 2 blue marbles. Probability is the number of wanted outcomes divided by the number of possible outcomes: 2/6, which simplifies to 1/3.

The spinner is split into 8 equal parts: 3 orange, 1 blue and 4 green. Because the parts are equal, every part has the same chance. The probability of orange is 3/8.

A die has 6 faces, and no face is favoured. Outcomes like these are called equally likely. When outcomes are equally likely, each one has the same probability: on a die, every number has a probability of 1/6.

Now we roll the die and we want an odd number. The wanted outcomes are 1, 3 and 5. That is 3 outcomes. There are 6 possible outcomes. The probability is 3/6 = 1/2.

Probability is always between 0 and 1. Rolling a 7 on a die is an impossible event: its probability is 0. Rolling a number from 1 to 6 is a certain event: its probability is 1. Rolling an odd number is halfway between them: 1/2.

The probability that an event happens and the probability that it does not happen always add up to 1. If the probability of picking blue is 2/6, the probability of not picking blue is 4/6. 2/6 + 4/6 = 1.

There are 2 blue and 4 red marbles in the bag. The probability of blue is 2/6 = 1/3. Let’s put 2 more blue marbles in. Now there are 8 marbles, and 4 of them are blue: the probability is 4/8 = 1/2. Adding blue marbles increases the chance of picking blue.

A bag has 1 blue and 3 red marbles. By calculation, the probability of blue is 1/4, which is 0.25. In an experiment, we put the marble back after every draw. In 20 draws we got 7 blues: 0.35. In 200 draws we got 52 blues: 0.26. The more draws we make, the closer the experiment gets to the calculation.

Summary: the possible outcomes are all the results. Probability is the number of wanted outcomes divided by the number of possible outcomes. The probability of an impossible event is 0, and of a certain event it is 1. The probabilities of happening and not happening add up to 1. Now try it in Graphs and Chance!