Chance and Probability

In short: Probability is how likely something is, from 0 (impossible) to 1 (certain). When every outcome is equally likely, the probability is the number of ways it can happen over the total number of outcomes. If an item is taken out and not put back, the total goes down for the next pick.

Before you start

Simplifying fractions (see Types of Fractions and Equivalent Fractions).
Fractions, decimals and percentages (see Fractions, Decimals and Percentages).

Words for chance

Word	Probability
Impossible	0
Unlikely	between 0 and $\frac{1}{2}$
Even chance	$\frac{1}{2}$
Likely	between $\frac{1}{2}$ and 1
Certain	1

Probability as a fraction

Spinners and dice

On a fair dice, each number from 1 to 6 has a probability of $\frac{1}{6}$ . The chance of an even number is $\frac{3}{6} = \frac{1}{2}$ .

A spinner has 8 equal sections. If 3 of them show a number bigger than 0.5, the chance of landing on one is $\frac{3}{8}$ . Only count sections, not colours or sizes, when the sections are equal.

Working backwards

Not putting it back

Probability

Scale

0 impossible
1/2 even chance
1 certain

Fraction

Ways over total
All add to 1
Not = 1 minus

Backwards

From probability to count
Use parts for ratios

Without replacement

Total goes down
One fewer of that kind

Quick summary

Probability goes from 0 (impossible) to 1 (certain).
Probability $=$ ways it can happen $\div$ total outcomes.
The probabilities of all outcomes add to 1, so P(not A) $= 1 -$ P(A).
Work backwards: probability $\times$ total gives how many.
Without replacement, the total and that kind each go down by 1 for the next pick.

Quiz

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Try 3 questions now

A bag has 3 red and 5 green balls. What is the probability of picking red?
1. A $\frac{3}{5}$
2. B $\frac{3}{8}$
3. C $\frac{5}{8}$
4. D $\frac{1}{3}$
Show answer
B: $\frac{3}{8}$
3 red out of 8 balls.
What is the probability of rolling a 7 on a normal dice?
1. A 0
2. B $\frac{1}{7}$
3. C $\frac{1}{6}$
4. D 1
Show answer
A: 0
A dice only has 1 to 6, so it is impossible.
What is the probability of rolling an even number on a dice?
1. A $\frac{1}{6}$
2. B $\frac{1}{3}$
3. C $\frac{1}{2}$
4. D $\frac{2}{3}$
Show answer
C: $\frac{1}{2}$
2, 4 and 6: three out of six.