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

Free Practice Question

PS · Problem Solving

705-805

Probability

If a fair coin is flipped six times, what is the probability of obtaining 'tails' no more than once in the six flips? This is a problem-solving question.

Answer Choices

Correct answer marked below

\frac{7}{64}

Correct

\frac{1}{64}

\frac{21}{64}

\frac{15}{64}

\frac{6}{64}

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Explanation

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Official Explanation

Official

To solve the problem of finding the probability of obtaining 'tails' no more than once in six flips of a fair coin, we can follow these steps:

Step 1: Determine the Total Number of Possible Outcomes

Each flip of a fair coin has 2 possible outcomes: heads (H) or tails (T). Since the coin is flipped six times, the total number of possible outcomes is:

2^6 = 64

Step 2: Determine the Number of Favorable Outcomes

We want to find the number of outcomes where 'tails' appears no more than once. This means we are interested in two scenarios:

No tails (all heads): There is only 1 such outcome: HHHHHH.

Exactly one tail: The tail can appear in any one of the six flips. For each position where the tail appears, the rest of the flips must be heads. Therefore, there are 6 possible outcomes:…

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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.