Step by step
The question
Question: A bag has 3 red and 5 blue marbles.
One marble is picked without looking.
What are the odds for it being red?
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
So there are 8 outcomes in all, each just as likely.
all = 8
2 Count for and against
The outcomes we want: red marbles.
3 outcomes are for.
for = 3
All the others are against: 8 minus 3 is 5.
against = 8 − 3 = 5
3 Write the odds
For, then against: 3 to 5.
odds for = 3 : 5
Careful!
Odds compare for with against.
Not with all 8.
3/8 would be a probability.
Careful: not 3 : 8 ✗
4 Check
Let's check: for and against together are 3 plus 5, that is 8.
Every outcome is counted once.
So the answer is right!
for + against = 3 + 5 = 8 = all
Let's look back.
First: count the outcomes.
Then: count for and against.
Then: write the odds.
Last: check.
Answer
Careful: not 3 : 8 ✗