Question

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

Answer 1

`P(H,H) = 1/4`

Explanation:

There are several possibilities:

tail, tail
tail, head
head, tail
head, head

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 `2/4=1/2` because there are two ways for the two coins to yield the mixed results.)

Answer 2

`P(H,H) = 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(H,H) = P(H) " AND " P(H)" "larr` 'and' means multiply

`P(H) xx P(H) = 1/2 xx 1/2 = 1/4`