Flip 3 coins, P(exactly 1 head) Step by Step

Step by step

The question

Question: 3 coins are flipped.

What is the probability of getting exactly 1 head?

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

P(exactly 1 head) = 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 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 Count the ones we want

Outcomes with exactly 1 head: HTT, THT and TTH.

That is 3 outcomes we want.

we want = 3

3 Write the fraction

3 we want, out of 8.

So the probability is 3/8.

P(exactly 1 head) = 38

Careful!

0, 1, 2 or 3 heads are not equally likely.

HT and TH are two different outcomes.

Careful: not 14 ✗

4 Check

Let's check with the others.

8 minus 3 is 5.

3/8 plus 5/8 is 8/8: that is 1, all of them.

So the answer is right!

P(exactly 1 head) + P(not exactly 1 head) = 38 + 58 = 88 = 1

Let's look back.

First: list all outcomes.

Then: count the ones we want.

Then: write the fraction.

Last: check.

Answer