Step by step
The question
Question: find the odds against rain, when the probability of rain is 80%.
P(rain) = 80%
The odds against put the outcomes against first, then the outcomes for.
odds against = against : for
1 Make it a fraction
Percent means out of 100: 80% is 80/100.
P(rain) = 80100
Both 80 and 100 can be divided by 20.
That makes it simpler.
P(rain) = 80 ÷ 20100 ÷ 20
So it is 4/5.
P(rain) = 45
2 Read the fraction
4/5 means 4 out of every 5 outcomes are for rain.
for = 4
The others are against: 5 minus 4 is 1.
against = 5 − 4 = 1
3 Write the odds
Against, then for: 1 to 4.
odds against = 1 : 4
Careful!
The 5 is all the outcomes.
Odds compare for with against, not with all.
Careful: not 1 : 5 ✗
4 Check
Let's check by going back.
The probability is for over all: 4/4 plus 1.
That is 4/5.
The same.
So the answer is right!
P = for over all = 44 + 1 = 45 ✓
Let's look back.
First: make it a fraction.
Then: read the fraction.
Then: write the odds.
Last: check.
Answer
Careful: not 1 : 5 ✗