AMC 8 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 18 Medium

In the sixth grade of a certain primary school, there are 6 classes, each with 40 students. Two classes are randomly selected from the 6 classes to participate in a live entertainment event hosted by a TV station. During the event, there is one lottery in which 4 lucky audience members are chosen. What is the probability that Bunny, a sixth-grade student, becomes one of the lucky winners?

  • A.

    \frac{1}{60}

  • B.

    \frac{1}{20}

  • C.

    \frac{1}{30}

  • D.

    \frac{1}{15}

  • E.

    \frac{1}{10}

Answer:A

The probability that Bunny’s class is selected to participate in the event is \frac{_{5}C_{1}}{_{6}C_{2}} = \frac{5}{15} = \frac{1}{3}.

If Bunny participates in the event, then the probability that he becomes a lucky winner is \frac{4}{40 \times 2} = \frac{1}{20}.

 

Therefore, the probability that Bunny becomes a lucky winner is \frac{1}{3} \times \frac{1}{20} = \frac{1}{60}.

Alternatively, the probability that Bunny’s class is selected can also be written as \frac{5}{6 \times 5 \div 2} = \frac{1}{3}.

Then, combining with the lottery probability, we again obtain \frac{1}{3} \times \frac{1}{20} = \frac{1}{60}.

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