A fair coin is flipped six times. What is the probability of obtaining 'tails' no more than once in the six flips?

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\frac{7}{64}

Correct

\frac{1}{6}

\frac{1}{2}

\frac{1}{64}

\frac{21}{32}

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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 in six flips of a fair coin, we can follow these steps:

Step 1: Determine the Total Number of Possible Outcomes

When a fair coin is flipped six times, each flip has 2 possible outcomes: heads (H) or tails (T). Therefore, the total number of possible outcomes for six flips is:

2^6 = 64

Step 2: Determine the Number of Desired 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 flips result in heads.

Exactly one tail: One flip results in tails, and the other five flips result in heads.

Scenario 1: No Tails

There is only one outcome where all flips are heads:…

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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.