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Omni-MATH / Kelvin and 15 other frogs are in a meeting, for a total of 16 frogs. During the…

Problem

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problem

Kelvin and 15 other frogs are in a meeting, for a total of 16 frogs. During the meeting, each pair of distinct frogs becomes friends with probability 12\frac{1}{2}. Kelvin thinks the situation after the meeting is cool if for each of the 16 frogs, the number of friends they made during the meeting is a multiple of 4. Say that the probability of the situation being cool can be expressed in the form ab\frac{a}{b}, where aa and bb are relatively prime. Find aa.
Plain-text mathematical notation (without MathML)
Kelvin and 15 other frogs are in a meeting, for a total of 16 frogs. During the meeting, each pair of distinct frogs becomes friends with probability (1)/(2). Kelvin thinks the situation after the meeting is cool if for each of the 16 frogs, the number of friends they made during the meeting is a multiple of 4. Say that the probability of the situation being cool can be expressed in the form (a)/(b), where a and b are relatively prime. Find a.
Original LaTeX notation
Kelvin and 15 other frogs are in a meeting, for a total of 16 frogs. During the meeting, each pair of distinct frogs becomes friends with probability $\frac{1}{2}$. Kelvin thinks the situation after the meeting is cool if for each of the 16 frogs, the number of friends they made during the meeting is a multiple of 4. Say that the probability of the situation being cool can be expressed in the form $\frac{a}{b}$, where $a$ and $b$ are relatively prime. Find $a$.

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Source and history

task_id
3c320d26-c8b1-5af4-a6fa-04b31b745905
task_key
test--3c320d26-c8b1-5af4-a6fa-04b31b745905
task_revision_id
1
config / split
/ test

Official source

initial import