The odds for win are 4 : 6, find P(win) Step by Step

Step by step

The question

Question: find the probability of win, when the odds for win are 4 to 6.

odds for = 4 : 6

The odds for are the outcomes for, to the outcomes against.

odds for = for : against

1 For and against

So 4 outcomes are for win.

for = 4

And 6 are against.

against = 6

2 Add for all

All the outcomes: for plus against.

4 plus 6 is 10.

all = 4 + 6 = 10

3 Write the fraction

The probability is for over all: 4/10.

P(win) = 410

Careful!

The bottom is all the outcomes, for plus against: 10.

Not only the 6 against.

Careful: not 46 ✗

4 Simplify

Both 4 and 10 can be divided by 2.

That makes it simpler.

P(win) = 4 ÷ 210 ÷ 2

So it is 2/5.

P(win) = 25

5 Check

Let's check by going back.

2 out of 5 are for, and 3 against.

The odds for: 2 to 3.

for: 2 of 5, against: 5 − 2 = 3 → 2 : 3

And 4 to 6 simplifies to the same.

So the answer is right!

4 : 6 = 2 : 3 ✓

Let's look back.

First: for and against.

Then: add for all.

Then: write the fraction.

Then: simplify.

Last: check.

Answer