Flip 3 coins, odds for exactly 2 heads Step by Step

Step by step

The question

Question: 3 coins are flipped.

What are the odds for getting exactly 2 heads?

The odds for something compare the outcomes for it, with the outcomes against it.

odds for = for : against

For: the outcomes we want.

Against: all the others.

for = we want, against = the others

1 Count the outcomes

Each coin lands heads, H, or tails, T.

Here is every outcome.

So there are 8 outcomes in all, each just as likely.

all = 8

2 Count for and against

The outcomes we want: outcomes with exactly 2 heads.

3 outcomes are for.

for = 3

All the others are against: 8 minus 3 is 5.

against = 8 − 3 = 5

3 Write the odds

For, then against: 3 to 5.

odds for = 3 : 5

Careful!

Odds compare for with against.

Not with all 8.

3/8 would be a probability.

Careful: not 3 : 8 ✗

4 Check

Let's check: for and against together are 3 plus 5, that is 8.

Every outcome is counted once.

So the answer is right!

for + against = 3 + 5 = 8 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Last: check.

Answer