Dear Math Circler,
The AMC 10B and AMC 12B contests are just days away!
Join us at Bard College on Wednesday, February 13, 2019 for the AMC 10/12 B contests. The event starts at 4 pm and will finish by 7 pm. This event is free, but space is limited. Please register in advance.
The AMC 12B may already be full, and we expect the AMC 10B to fill as well. If you find yourself waitlisted, please email us at bardmathcircle@gmail.com.
Yet another favorite problem from last year's contest:
A box contains 5 chips, numbered 1, 2, 3, 4, and 5. Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds 4. What is the probability that 3 draws are required?
(A) 1/15 (B) 1/10 (C) 1/6 (D) 1/5 (E) 1/4
See below for a solution.
What are the AMC 10B and 12B?
The American Mathematics Competitions are a series of examinations that build problem-solving skills and mathematical knowledge in middle and high school students. Each of the AMC 10 (grades 10 and below, under 17.5 years of age) and AMC 12 (grades 12 and below, under 19.5 years of age) contests is 25 multiple choice questions long and runs for 75 minutes. The contest problems are accessible, yet go above and beyond the high school curriculum in both depth and level of challenge. To enjoy the AMC experience and grow mathematically, students are recommended to prepare, for example by solving past AMC 10 and AMC 12 contest problems.
The Bard Math Circle offers the B version of the exams on February 13, 2019. (The A version runs the week before on February 7.)
Join us after the contest for refreshments, and a mathematical conversation.
We can't wait to see you at the AMC 10/12B!
Bard Math Circle
A solution to yet another favorite problem from last year's contest:
Let's phrase the question another way: if 3 draws are required for the sum to exceed 4, then 2 draws don't suffice. So we list the ways to draw two chips so that their sum does not exceed 4. There are 4 ways to do this: 1 + 2, 2 + 1, 1 + 3, and 3 + 1.
The total number of ways to draw two chips is 5×4 (there are 5 choices for the first draw, and 4 choices left for the second draw).
The final probability, is 4/(5×4) = 1/5. Therefore, the correct answer is (D).
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