If a fair coin is flipped four times, what is the probability of obtaining 'tails' no more than once in the four flips? $\text{Express your answer as a simplified fraction.}$

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\frac{1}{2}

\frac{7}{16}

\frac{1}{4}

\frac{3}{8}

\frac{5}{16}

Correct

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Explanation

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Official Explanation

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To determine the probability of obtaining 'tails' no more than once when a fair coin is flipped four times, follow these steps:

Total Possible Outcomes:

Each coin flip has 2 possible outcomes: heads (H) or tails (T). For four flips, the total number of possible outcomes is:

2^4 = 16

Desired Outcomes:

We want the number of outcomes where 'tails' appears no more than once. This includes:

- 0 tails: All four flips are heads (HHHH).

- 1 tail: One flip is tails and the other three are heads. The tail can occur in any one of the four positions (THHH, HTHH, HHTH, HHHT).…

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What this question tests

What it tests

Your ability to compute probabilities of single and compound events, including 'at least one' questions.

Common trap

Forgetting to use the complement for 'at least one', or treating dependent events as independent.

If a fair coin is flipped four times, what is the probability of obtaining 'tails' no more than once in the four flips? Express your answer as a simplified fraction.\text{Express your answer as a simplified fraction.}Express your answer as a simplified fraction.