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Omni-MATH / A box contains twelve balls, each of a different color. Every minute, Randall…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A box contains twelve balls, each of a different color. Every minute, Randall randomly draws a ball from the box, notes its color, and then returns it to the box. Consider the following two conditions: (1) Some ball has been drawn at least twelve times (not necessarily consecutively). (2) Every ball has been drawn at least once. What is the probability that condition (1) is met before condition (2)? If the correct answer is CC and your answer is AA, you get max(⌊30(1−12|log2C−log2A|)⌋,0)\max \left(\left\lfloor 30\left(1-\frac{1}{2}\left|\log _{2} C-\log _{2} A\right|\right)\right\rfloor, 0\right) points.
Plain-text mathematical notation (without MathML)
A box contains twelve balls, each of a different color. Every minute, Randall randomly draws a ball from the box, notes its color, and then returns it to the box. Consider the following two conditions: (1) Some ball has been drawn at least twelve times (not necessarily consecutively). (2) Every ball has been drawn at least once. What is the probability that condition (1) is met before condition (2)? If the correct answer is C and your answer is A, you get max(⌊30(1−(1)/(2)|log₂C−log₂A|)⌋,0) points.
Original LaTeX notation
A box contains twelve balls, each of a different color. Every minute, Randall randomly draws a ball from the box, notes its color, and then returns it to the box. Consider the following two conditions: (1) Some ball has been drawn at least twelve times (not necessarily consecutively). (2) Every ball has been drawn at least once. What is the probability that condition (1) is met before condition (2)? If the correct answer is $C$ and your answer is $A$, you get $\max \left(\left\lfloor 30\left(1-\frac{1}{2}\left|\log _{2} C-\log _{2} A\right|\right)\right\rfloor, 0\right)$ points.

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Source and history

task_id
cd9366cc-313f-59e3-a2a6-7ff5a5f1d0c5
task_key
test--cd9366cc-313f-59e3-a2a6-7ff5a5f1d0c5
task_revision_id
1
config / split
/ test

Official source

initial import