If a fair coin is flipped four times, what is… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Probability

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

Correct answer marked below

\frac{5}{16}

Correct

\frac{1}{4}

\frac{3}{8}

\frac{7}{16}

\frac{1}{2}

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Explanation

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Official Explanation

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

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

We want the number of tails to be no more than once, which means:

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

1 tail: Exactly one flip is tails, and the other three are heads. The tail can occur in any one of the four positions:…

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What this question tests

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

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