Step by step
The question
Question: find the odds against rain, when the probability of rain is 2/7.
P(rain) = 27
The odds against put the outcomes against first, then the outcomes for.
odds against = against : for
1 Read the fraction
2/7 means 2 out of every 7 outcomes are for rain.
for = 2
The others are against: 7 minus 2 is 5.
against = 7 − 2 = 5
2 Write the odds
Against, then for: 5 to 2.
odds against = 5 : 2
Careful!
The 7 is all the outcomes.
Odds compare for with against, not with all.
Careful: not 5 : 7 ✗
3 Check
Let's check by going back.
The probability is for over all: 2/2 plus 5.
That is 2/7.
The same.
So the answer is right!
P = for over all = 22 + 5 = 27 ✓
Let's look back.
First: read the fraction.
Then: write the odds.
Last: check.
Answer
Careful: not 5 : 7 ✗