A fair coin is tossed four times. What is the probability of getting exactly two heads?

\frac{3}{8}

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

\frac{5}{8}

Correct answerYour answer

\frac{11}{16}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Four tosses give $2^4 = 16$ equally likely sequences.
Sequences with exactly two heads: ${}^{4}C_{2} = 6$ .
Probability $= \frac{6}{16} = \frac{3}{8}$ .

Worth noting

$\frac{1}{2}$ assumes 'half heads' is the typical result, so its chance must be a half. $\frac{11}{16}$ is P(at least two heads) and $\frac{5}{8}$ is P(not exactly two).

Concept: Counting coin sequences with combinations
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsCoins, dice and cards

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A fair coin is tossed four times. What is the probability of getting exactly two heads?

Explanation