AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 24 Medium

Since Wong is busy at work and has no time to cook lunch, he orders takeout. Suppose both Wong and the delivery person both arrive randomly between 12{:}00 and 12{:}10 at the entrance of Wong’s building. Suppose Wong arrived earlier than the delivery person, what is the probability that Wong waits no more than 5 minutes for the delivery person?

  • A.

    \frac{1}{2}

  • B.

    \frac{4}{5}

  • C.

    \frac{3}{4}

  • D.

    \frac{3}{8}

  • E.

    \frac{5}{8}

Answer:C

Let the arrival times (in minutes after 12:00) of the delivery person and Wong be x and y respectively. The event that “Wong waits no more than 5 minutes” is event A.

 

The sample space is \Omega = \{(x,y)\;|\;0 \leq x \leq 10,\;0 \leq y \leq 10\}, and A = \{(x,y)\;|\;0 \leq x \leq 10,\;0 \leq y \leq 10,\;0 \leq y-x \leq 5\}.

 

(see figure)

P(A)=\frac{\dfrac{1}{2}(10\times 10-5\times 5)}{\frac{1}{2}\times 10\times 10}=\frac{3}{4}．

Choose \text{C}.

Related Problems
Problem 22 AMC 10 Weekly Practice Round 3
Problem 23 AMC 10 Weekly Practice Round 3
Problem 25 AMC 10 Weekly Practice Round 3
Problem 26 AMC 10 Weekly Practice Round 3
Think Academy Powered by ChatGPT