Step by step
The question
Question: find the odds for win, when the probability of win is 0.25.
P(win) = 0.25
The odds for compare the outcomes for, with the outcomes against.
odds for = for : against
1 Make it a fraction
0.25 is 25/100.
P(win) = 25100
Both 25 and 100 can be divided by 25.
That makes it simpler.
P(win) = 25 ÷ 25100 ÷ 25
So it is 1/4.
P(win) = 14
2 Read the fraction
1/4 means 1 out of every 4 outcomes are for win.
for = 1
The others are against: 4 minus 1 is 3.
against = 4 − 1 = 3
3 Write the odds
For, then against: 1 to 3.
odds for = 1 : 3
Careful!
The 4 is all the outcomes.
Odds compare for with against, not with all.
Careful: not 1 : 4 ✗
4 Check
Let's check by going back.
The probability is for over all: 1/1 plus 3.
That is 1/4.
The same.
So the answer is right!
P = for over all = 11 + 3 = 14 ✓
Let's look back.
First: make it a fraction.
Then: read the fraction.
Then: write the odds.
Last: check.
Answer
Careful: not 1 : 4 ✗