Flip 2 coins, P(no heads) Step by Step

Step by step

The question

Question: 2 coins are flipped.

What is the probability of getting no heads?

The probability is a fraction: the outcomes we want, over all the outcomes.

P(no heads) = we wantall

P stands for probability.

P = probability

1 List all outcomes

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

Here is every outcome.

Each coin has 2 ways.

2 times 2 is 4 outcomes, all just as likely.

all = 2 × 2 = 4

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

H = heads, T = tails

sample space = all the outcomes

2 Count the ones we want

Outcomes with no heads: just one.

That is 1 outcome we want.

we want = 1

3 Write the fraction

1 we want, out of 4.

So the probability is 1/4.

P(no heads) = 14

Careful!

0, 1 or 2 heads are not equally likely.

HT and TH are two different outcomes.

Careful: not 13 ✗

4 Check

Let's check with the others.

4 minus 1 is 3.

1/4 plus 3/4 is 4/4: that is 1, all of them.

So the answer is right!

P(no heads) + P(not no heads) = 14 + 34 = 44 = 1

Let's look back.

First: list all outcomes.

Then: count the ones we want.

Then: write the fraction.

Last: check.

Answer