Complementary events
The question
2 red, 6 blue, 4 green — P(not red)
2 + 6 + 4=12
2 + 6 + 4=12
red:2
not red:12 − 2 =10
2 + 6 + 4=12
not red:10
+=
which is1
2 + 6 + 4=12
=
- Count everything first: 2 + 6 + 4 = 12 altogether. That is the bottom of the fraction.
- Read the question again: it asks for not red. So the wins are everything else — all 12 except the 2 red, which is 12 − 2 = 10.
- Chance is the wins over the total. So it is 10 out of 12.
- Check it: the chance of red and the chance of not red have to fill the bag between them. 2 out of 12 and 10 out of 12 make 12 out of 12 — the whole bag.
- And can be written in bigger pieces: .
How it works.
- 01
Count everything first: 2 + 6 + 4 = 12 altogether. That is the bottom of the fraction.
- 02
Read the question again: it asks for not red. So the wins are everything else — all 12 except the 2 red, which is 12 − 2 = 10.
- 03
Chance is the wins over the total. So it is 10 out of 12.
- 04
Check it: the chance of red and the chance of not red have to fill the bag between them. 2 out of 12 and 10 out of 12 make 12 out of 12 — the whole bag.
- 05
And 10/12 can be written in bigger pieces: 5/6.