The odds against win are 15 : 5, find P(win) Step by Step

Step by step

The question

Question: find the probability of win, when the odds against win are 15 to 5.

odds against = 15 : 5

The odds against put the outcomes against first, then the outcomes for.

odds against = against : for

1 For and against

Against comes first.

So 15 are against, and 5 are for.

for = 5

against = 15

2 Add for all

All the outcomes: for plus against.

5 plus 15 is 20.

all = 5 + 15 = 20

3 Write the fraction

The probability is for over all: 5/20.

P(win) = 520

Careful!

The bottom is all the outcomes, for plus against: 20.

Not only the 15 against.

Careful: not 515 ✗

4 Simplify

Both 5 and 20 can be divided by 5.

That makes it simpler.

P(win) = 5 ÷ 520 ÷ 5

So it is 1/4.

P(win) = 14

5 Check

Let's check by going back.

1 out of 4 are for, and 3 against.

The odds against: 3 to 1.

for: 1 of 4, against: 4 − 1 = 3 → 3 : 1

And 15 to 5 simplifies to the same.

So the answer is right!

15 : 5 = 3 : 1 ✓

Let's look back.

First: for and against.

Then: add for all.

Then: write the fraction.

Then: simplify.

Last: check.

Answer