Mathematics (Core)Exam code: 0580
Basic Probability
Probability
Equally likely outcomes
- With equally likely outcomes, count how many produce the event and divide that count by how many outcomes there are altogether
- Count the total carefully, since it is the denominator of everything that follows
- A bag holds 40 counters of which 14 are red, so the probability of drawing a red one is 14 ÷ 40, which simplifies to 7/20
- Simplifying is not required unless the question asks for the simplest form: the mark schemes accept any equivalent fraction, such as 14/40
- Information may come from a table, a graph or a Venn diagram rather than from a sentence
Probabilities that must add to 1
- Every outcome of an experiment together accounts for the whole of the probability, so they add to 1
- A table with one probability missing is completed by subtracting the others from 1
- The event not happening takes up whatever is left, so for an event A, the probability of A not happening is 1 − the probability of A happening, written P(not A) = 1 − P(A) for short
- Where a train has a 0.28 chance of being late, the chance of it not being late is 1 − 0.28 = 0.72
- Events that can never occur together are mutually exclusive, and for those the chance of one or the other is simply the sum of the two
- An event and its complement are always mutually exclusive, which is why they add to 1
Exam tip
Write the subtraction from 1
When a probability table has a gap, the subtraction from 1, such as 1 − (0.3 + 0.25), earns a method mark on its own, even if a later step slips, so write it as a line first. If two gaps are linked, as in "green is twice as likely as yellow", share the 0.45 that is left, not 1: green takes 2 parts and yellow 1, so yellow is 0.45 ÷ 3 = 0.15 and green 0.3.
Worked example
Completing a probability table
A bag holds beads that are red, blue, green or yellow. A bead is taken at random. The table shows the probabilities of red, blue and green. Find the probability of yellow, and the probability of taking a green or a yellow bead.
| Colour | red | blue | green | yellow |
|---|---|---|---|---|
| Probability | 0.35 | 0.2 | 0.15 |
Solution:
- The four probabilities together must come to 1
- The three given ones total 0.35 + 0.2 + 0.15 = 0.7
- So the probability of yellow is 1 − 0.7 = 0.3
- One bead cannot be both green and yellow, so those events are mutually exclusive and their probabilities add
- P(green or yellow) = 0.15 + 0.3 = 0.45