Probability, step by step
The chance of one thing happening is how many ways it can, over how many ways anything can.
The question
3 red, 6 blue, 3 green — P(green)
3 + 6 + 3=12
3 + 6 + 3=12
green:3
3 + 6 + 3=12
green:3
3 + 6 + 3=12
=
- Count EVERYTHING first, before the ones being asked about: 3 + 6 + 3 = 12 altogether. That is the bottom of the fraction, and it is the half that gets swapped for the wrong number.
- Now the ones that count as a win: 3 green.
- Chance is the wins OVER the total — not over the rest. So it is 3 out of 12.
- And 3/12 can be written in bigger pieces: 1/4.
How it works.
- 01
Count EVERYTHING first, before the ones being asked about: 3 + 6 + 3 = 12 altogether. That is the bottom of the fraction, and it is the half that gets swapped for the wrong number.
- 02
Now the ones that count as a win: 3 green.
- 03
Chance is the wins OVER the total — not over the rest. So it is 3 out of 12.
- 04
And 3/12 can be written in bigger pieces: 1/4.