A box holds 60 pens. One pen is taken at random and the probability that it is black is 0.45. How many pens in the box are not black?
- P(not black) = 1 − 0.45 = 0.55.
- Number not black = 0.55 × 60.
- 0.55 × 60 = 33.
Answer: 33 pens
Introduction to probability
Maths · Probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
Probability measures how likely an event is, on a scale from 0 to 1. A probability of 0 means the event is impossible and 1 means it is certain. No probability can be negative or greater than 1.
When all outcomes are equally likely, for example with a fair dice or a counter taken at random, count the outcomes you want and divide by the total number of outcomes.
P(A) means the probability that event A happens. P(A′) means the probability that A does not happen. An event either happens or does not, so these two add up to 1. In the same way, the probabilities of all the possible outcomes of an experiment add up to 1.
Rules to remember
- P(event) = number of outcomes you want ÷ total number of equally likely outcomes
- 0 ≤ P(event) ≤ 1: impossible = 0, certain = 1
- P(not A) = 1 − P(A), also written P(A′) = 1 − P(A)
- The probabilities of all the outcomes add up to 1, when only one of them can happen at a time
- Number of items of one kind = P(that kind) × total number of items
- Total number of items = number of one kind ÷ P(that kind)
- Give a probability as a fraction, decimal or percentage, not as a ratio
Common mistake
Students count the different kinds of outcome, not every outcome. In a word with repeated letters, or a bag with several counters of one colour, each letter or counter counts separately in the total.
Worked example
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