AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 20 Medium

Weier is playing a coin-tossing game: If a coin is tossed 5 times, what is the probability of getting heads no more than twice?

  • A.

    \frac{1}{2}

  • B.

    \frac{1}{8}

  • C.

    \frac{5}{32}

  • D.

    \frac{1}{32}

  • E.

    \frac{1}{4}

Answer:A

The probability of getting 0 heads is \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{32}, the probability of getting 1 head is 5 \times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{5}{32}, the probability of getting 2 heads is _{5}C_{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{5}{16}.

Therefore, the probability of getting no more than 2 heads is \frac{1}{32}+\frac{5}{32}+\frac{5}{16}=\frac{1}{2}.

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