AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 30 Medium

A bag contains 5 balls that are identical in size and shape: 3 white balls and 2 red balls. Two balls are drawn with replacement. What is the probability that the two balls are of different colors?

  • A.

    \frac{2}{5}

  • B.

    \frac{11}{25}

  • C.

    \frac{12}{25}

  • D.

    \frac{13}{25}

  • E.

    \frac{3}{5}

Answer:C

The probability that both balls are white is \frac{3 \times 3}{5 \times 5} = \frac{9}{25}, and the probability that both balls are red is \frac{2 \times 2}{5 \times 5} = \frac{4}{25}.

So the probability that the two balls are the same color is \frac{9}{25} + \frac{4}{25} = \frac{13}{25}.

Therefore, the probability that the two balls are of different colors is 1 - \frac{13}{25} = \frac{12}{25}.

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