Step by step
The question
Question: find the probability of a, when the odds for a are 3 to 5.
odds for = 3 : 5
The odds for are the outcomes for, to the outcomes against.
odds for = for : against
1 For and against
So 3 outcomes are for a.
for = 3
And 5 are against.
against = 5
2 Add for all
All the outcomes: for plus against.
3 plus 5 is 8.
all = 3 + 5 = 8
3 Write the fraction
The probability is for over all: 3/8.
P(a) = 38
Careful!
The bottom is all the outcomes, for plus against: 8.
Not only the 5 against.
Careful: not 35 ✗
4 Check
Let's check by going back.
3 out of 8 are for, and 5 against.
The odds for: 3 to 5.
The same as the question.
So the answer is right!
for: 3 of 8, against: 8 − 3 = 5 → 3 : 5 ✓
Let's look back.
First: for and against.
Then: add for all.
Then: write the fraction.
Last: check.
Answer
Careful: not 35 ✗