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

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

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Answer 1 · 2016-02-23T21:40:28

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

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:

$1 in 4 = 0.25 = 25 % = \frac{1}{4}$ $1 " in " 4 = 0.25 " = 25% = 1/4$

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 $2 in 4 = 0.50 = 50 %$ $2 " in " 4 = 0.50 = 50%$ or $\frac{2}{4} = \frac{1}{2}$ $2/4=1/2$ because there are two ways for the two coins to yield the mixed results.)

Answer 2 · 2017-03-15T12:54:16

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

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.

$P (H, H) = P (H) AND P (H) \leftarrow$ $P(H,H) = P(H) " AND " P(H)" "larr$ 'and' means multiply

$P (H) \times P (H) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ $P(H) xx P(H) = 1/2 xx 1/2 = 1/4$

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

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