Step by step
The question
Question: find the odds for win, when the probability of win is 3/8.
P(win) = 38
The odds for compare the outcomes for, with the outcomes against.
odds for = for : against
1 Read the fraction
3/8 means 3 out of every 8 outcomes are for win.
for = 3
The others are against: 8 minus 3 is 5.
against = 8 − 3 = 5
2 Write the odds
For, then against: 3 to 5.
odds for = 3 : 5
Careful!
The 8 is all the outcomes.
Odds compare for with against, not with all.
Careful: not 3 : 8 ✗
3 Check
Let's check by going back.
The probability is for over all: 3/3 plus 5.
That is 3/8.
The same.
So the answer is right!
P = for over all = 33 + 5 = 38 ✓
Let's look back.
First: read the fraction.
Then: write the odds.
Last: check.
Answer
Careful: not 3 : 8 ✗