Difference between revisions of "2018 AMC 10B Problems/Problem 6"
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<math>\frac{1}{5} \cdot \frac{1}{2} \cdot 2 = \frac{1}{5}</math>, or <math>\boxed {D}</math> | <math>\frac{1}{5} \cdot \frac{1}{2} \cdot 2 = \frac{1}{5}</math>, or <math>\boxed {D}</math> | ||
− | ~Soccer_JAMS | + | ~Soccer_JAMS |
== Solution 3 (Inequalities) == | == Solution 3 (Inequalities) == |
Revision as of 23:15, 10 November 2023
Contents
[hide]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 the first two draws as that gives us insight into if a third draw is necessary. Also, note that it is necessary to draw a to have 3 draws, otherwise will be attainable in two or fewer 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
~Soccer_JAMS
Solution 3 (Inequalities)
We know that the first draws must be leaving us with with the only option being that and are chosen in either order. This means there is a probability of , or
~MC_ADe
Video Solution (HOW TO THINK CRITICALLY!!!)
~Education, the Study of Everything
Video Solution
~savannahsolver
Video Solution
https://youtu.be/wopflrvUN2c?t=20
See Also
2018 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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