2018 AMC 10B Problems/Problem 6
Contents
Problem
A box contains chips, numbered , , , , and . Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds . What is the probability that draws are required?
Solution 1
Notice that the only four ways such that draws are required are ; ; ; and . Notice that each of those cases has a chance, so the answer is , or .
Jonathan Xu (pi_is_delicious_69420)
Solution 2
We only have to analyze first two draws as that gives us insight on if third draw is necessary. Also, note that it is necessary to draw a in order to have 3 draws, otherwise will be attainable in two or less draws. So the probability of getting a is . It is necessary to pull either a or on the next draw and the probability of that is . But, the order of the draws can be switched so we get:
, or
By: Soccer_JAMS
Video Solution
~savannahsolver
Video Solution by OmegaLearn
https://youtu.be/wopflrvUN2c?t=20
~ pi_is_3.14
See Also
2018 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AMC 10 Problems and Solutions |
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