Step by step
The question
Question: A number from 1 to 10 is picked at random.
What are the odds for it being a multiple of 3?
The odds for something compare the outcomes for it, with the outcomes against it.
odds for = for : against
For: the outcomes we want.
Against: all the others.
for = we want, against = the others
1 Count the outcomes
The numbers are 1 to 10.
So there are 10 outcomes in all, each just as likely.
all = 10
2 Count for and against
The outcomes we want: multiples of 3.
3 outcomes are for.
for = 3
All the others are against: 10 minus 3 is 7.
against = 10 − 3 = 7
3 Write the odds
For, then against: 3 to 7.
odds for = 3 : 7
Careful!
Odds compare for with against.
Not with all 10.
3/10 would be a probability.
Careful: not 3 : 10 ✗
4 Check
Let's check: for and against together are 3 plus 7, that is 10.
Every outcome is counted once.
So the answer is right!
for + against = 3 + 7 = 10 = all
Let's look back.
First: count the outcomes.
Then: count for and against.
Then: write the odds.
Last: check.
Answer
Careful: not 3 : 10 ✗