From 0 to 1

The idea

Probability is measured on a scale from 0 to 1, so 0 ≤ P(E) ≤ 1: 0 means impossible, 1 means certain and 0.5 an even chance; most events lie strictly between 0 and 1, also expressed as percentages.

A line for chance

We can put chance on a number line. Let the line start at 0 and end at 1. Where do you think an event that is impossible goes? And one that is certain?

Which end of the line is for "impossible"?

• 0
• 1

Slide along the scale

Change the number of purple cards. The marker moves along the line. Visit impossible, even chance and certain.

The scale

Probability is measured from 0 to 1: 0 ≤ P(E) ≤ 1, where 0 means impossible, 1 means certain and 0.5 means an even chance.

Most events lie strictly between 0 and 1. A probability can also be written as a percentage: 0.75 is 75%, and 0.5 is 50%.

Notes

0 ≤ P(E) ≤ 1, where P(E) = 0 is impossible, P(E) = 1 is certain, P(E) = 0.5 is an even chance. Probabilities can also be given as percentages.

Check yourself

A deck has 6 cards and 3 are purple. What is the probability of drawing purple, as a decimal?

Answer: 0.5

3 out of 6 is a half, so the probability is 0.5, an even chance.

Your school wins the hockey match with probability 75%. Write this as a decimal.

Answer: 0.75

75% = 75 ÷ 100 = 0.75.

Which of these cannot be a probability?

If P(E) = 1, what do we know?

• 0. 0 is allowed: it means impossible.
• 0.9. 0.9 lies between 0 and 1, so it can be a probability.
• 1.3 — correct. Yes. A probability is never more than 1.
• E is certain to happen — correct. Yes. 1 is the top of the scale: certain.
• E is impossible. That is P(E) = 0.
• E has an even chance. An even chance is P(E) = 0.5.