# If two fair coins are tossed, what is the probability of getting two heads?

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4
Mar 15, 2017

$P \left(H , H\right) = \frac{1}{4}$

#### Explanation:

There are several possibilities:

tail, tail

Each of these four outcomes is equally probable, so each has a 1 in 4 chance. So the probability of getting two heads is:

 1 " in " 4 = 0.25 " = 25% = 1/4

Probabilities are usually given as fractions.

(Now, had the question been "What is the probability of getting one head and one tail?" - the answer would be 2 " in " 4 = 0.50 = 50% or $\frac{2}{4} = \frac{1}{2}$ because there are two ways for the two coins to yield the mixed results.)

Then teach the underlying concepts
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#### Explanation

Explain in detail...

#### Explanation:

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1
Mar 15, 2017

$P \left(H , H\right) = \frac{1}{4}$

#### Explanation:

The probability of getting 2 heads with 2 coins can be broken into 2 steps:

The first coin must show Heads AND
the second coin must show Heads.

$P \left(H , H\right) = P \left(H\right) \text{ AND " P(H)" } \leftarrow$ 'and' means multiply

$P \left(H\right) \times P \left(H\right) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

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