Flip 3 coins, P(at least 1 head) Step by Step

Step by step

The question

Question: 3 coins are flipped.

What is the probability of getting at least 1 head?

At least 1 head means every outcome except no heads.

So we find the probability of no heads first.

Then we take it from 1.

P(at least 1 head) = 1 − P(no heads)

P stands for probability.

All the outcomes together make 1.

P = probability

P(not A) = 1 − P(A)

1 List all outcomes

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

Here is every outcome.

Each coin has 2 ways.

2 times 2 times 2 is 8 outcomes, all just as likely.

all = 2 × 2 × 2 = 8

This list of all the outcomes is called the sample space.

H = heads, T = tails

sample space = all the outcomes

2 Find the opposite

Outcomes with no heads: just one.

That is 1 outcome.

no heads = 1

So the probability of no heads is 1/8.

P(no heads) = 18

3 Take it from 1

Now we take it from 1.

P(at least 1 head) = 1 − 18

Careful!

1 is all the outcomes: 8/8.

Careful: 1 = 88 (all of them)

So we write 1 as 8/8.

P(at least 1 head) = 88 − 18

Same bottoms: we take away the tops.

8 minus 1 is 7.

P(at least 1 head) = 78

4 Check

Let's check by counting the others straight away.

7 out of 8.

The same.

So the answer is right!

at least 1 head: 7 of 8 → 78

Let's look back.

First: list all outcomes.

Then: find the opposite.

Then: take it from 1.

Last: check.

Answer