Probability · Ordinary Level
The Basics & Sample Space
Ordinary Level · Class 1 · Tap NEXT to begin
Section 1 of 2
What is Probability?
Chance as a fraction
Probability is chance. $P(\text{event}) = \dfrac{\text{number of ways it can happen}}{\text{total number of outcomes}}$.
Worked example — three quick ones
Find the probability of (i) a tail on a coin; (ii) a $6$ on a die; (iii) an ace from a pack of $52$.
(i) $\tfrac{1}{2}$ ($50:50$, one in two)
(ii) $\tfrac{1}{6}$ (one side is a $6$)
(iii) $P(\text{ace}) = \tfrac{4}{52} = \tfrac{1}{13}$
$\tfrac{1}{2},\ \tfrac{1}{6},\ \tfrac{1}{13}$
The probability scale
Probability runs from $0$ to $1$: $0$ = impossible (no chance, $0\%$); $\tfrac{1}{2}$ = even ($50:50$); $1$ = certain (guaranteed, $100\%$).
Section 2 of 2
Sample Space
List every result
A sample space is all the possible results — write them all out. Order matters: a head-then-tail is different from a tail-then-head.
Worked example — two coins
Two coins are thrown. What is the probability of getting a tail and a head?
Sample space: $hh,\ tt,\ ht,\ th$ — $4$ possible results
A head and a tail happens twice ($ht$ and $th$)
$P = \tfrac{2}{4} = \tfrac{1}{2}$
$\tfrac{2}{4} = \tfrac{1}{2}$
That’s Class 1.
Probability as a fraction, the $0$-to-$1$ scale, and writing out a sample space. Class 2: counting with the AND and OR rules.