AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 26 Medium

A student’s shooting accuracy for one shot is \frac{9}{10}, and the probability of making two consecutive shots is \frac{1}{2}. If the student has just made a shot, then what is the probability that the next shot is also successful?

  • A.

    \frac{1}{5}

  • B.

    \frac{2}{5}

  • C.

    \frac{3}{5}

  • D.

    \frac{5}{9}

  • E.

    \frac{2}{9}

Answer:D

If A_{i} \ (i=1,2) denotes the event that the i-th shot is successful, then

P(A_{1})=\frac{9}{10}, P(A_{1}A_{2})=\frac{1}{2}.

Therefore, P(A_{2}\,|\,A_{1})=\frac{P(A_{1}A_{2})}{P(A_{1})}=\frac{5}{9}.

Thus, the answer is D.

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