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

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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? Use the formula $P(X \leq 1) = P(X = 0) + P(X = 1)$ to calculate the probability.

Answer Choices

Correct answer marked below

\frac{7}{64}

Correct

\frac{1}{64}

\frac{1}{32}

\frac{1}{16}

\frac{1}{8}

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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 use the binomial probability formula. The binomial probability formula is given by:

P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}

where:

-

n

is the number of trials (in this case, 6 flips),

-

k

is the number of successful outcomes (in this case, the number of tails),

-

p

is the probability of success on a single trial (for a fair coin,

p = 0.5

for tails),

-

\binom{n}{k}

is the binomial coefficient, which represents the number of ways to choose

k

successes out of

n

trials.

The problem asks for the probability of obtaining 'tails' no more than once, which means we need to calculate the probability of getting 0 tails or 1 tail in 6 flips. This can be expressed as:

P(X \leq 1) = P(X = 0) + P(X = 1)

Let's calculate each term separately.

1. Calculate $P(X = 0)$

This is the probability of getting 0 tails in 6 flips.…

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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 six times, what is the probability of obtaining 'tails' no more than once in the six flips? Use the formula P(X≤1)=P(X=0)+P(X=1)P(X \leq 1) = P(X = 0) + P(X = 1)P(X≤1)=P(X=0)+P(X=1) to calculate the probability.