Probability · Second Year
Probability
Second Year · The formula & listing outcomes · Tap NEXT to begin
Section 1 of 2
The Probability Formula
The formula
$P(E) = \dfrac{\text{number of ways it can happen}}{\text{total number of outcomes}}$, on a scale from $0$ (impossible) to $1$ (certain).
Worked example — a single die
A fair die is rolled. Find $P(\text{an even number})$.
Even numbers: $2, 4, 6$ — that is $3$ out of $6$
$P = \dfrac{3}{6}$
$\dfrac{3}{6} = \dfrac{1}{2}$
Now you try
You try
A bag has $5$ blue and $3$ green marbles. Find $P(\text{green})$.
Pen and paper out — try it before you reveal.
$P(\text{green}) = \dfrac{3}{5+3}$
$\dfrac{3}{8}$
$\dfrac{3}{8}$
Section 2 of 2
Listing Outcomes
You try
Two coins are flipped. Find $P(\text{two heads})$.
Pen and paper out — try it before you reveal.
Outcomes: HH, HT, TH, TT — $4$ in total
Two heads: just HH
$\dfrac{1}{4}$
$\dfrac{1}{4}$
That’s Probability.
The formula, and listing every equally-likely outcome to count what you want.