Step by step
The question
Question: find the probability of rain, when the odds against rain are 7 to 2.
odds against = 7 : 2
The odds against put the outcomes against first, then the outcomes for.
odds against = against : for
1 For and against
Against comes first.
So 7 are against, and 2 are for.
for = 2
against = 7
2 Add for all
All the outcomes: for plus against.
2 plus 7 is 9.
all = 2 + 7 = 9
3 Write the fraction
The probability is for over all: 2/9.
P(rain) = 29
Careful!
The bottom is all the outcomes, for plus against: 9.
Not only the 7 against.
Careful: not 27 ✗
4 Check
Let's check by going back.
2 out of 9 are for, and 7 against.
The odds against: 7 to 2.
The same as the question.
So the answer is right!
for: 2 of 9, against: 9 − 2 = 7 → 7 : 2 ✓
Let's look back.
First: for and against.
Then: add for all.
Then: write the fraction.
Last: check.
Answer
Careful: not 27 ✗