Step by step
The question
Question: find the odds against late, when the probability of late is 0.6.
P(late) = 0.6
The odds against put the outcomes against first, then the outcomes for.
odds against = against : for
1 Make it a fraction
0.6 is 6/10.
P(late) = 610
Both 6 and 10 can be divided by 2.
That makes it simpler.
P(late) = 6 ÷ 210 ÷ 2
So it is 3/5.
P(late) = 35
2 Read the fraction
3/5 means 3 out of every 5 outcomes are for late.
for = 3
The others are against: 5 minus 3 is 2.
against = 5 − 3 = 2
3 Write the odds
Against, then for: 2 to 3.
odds against = 2 : 3
Careful!
The 5 is all the outcomes.
Odds compare for with against, not with all.
Careful: not 2 : 5 ✗
4 Check
Let's check by going back.
The probability is for over all: 3/3 plus 2.
That is 3/5.
The same.
So the answer is right!
P = for over all = 33 + 2 = 35 ✓
Let's look back.
First: make it a fraction.
Then: read the fraction.
Then: write the odds.
Last: check.
Answer
Careful: not 2 : 5 ✗