benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Bob the bomb-defuser has stumbled upon an active bomb. He opens it up, and finds…

Problem

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

problem

Bob the bomb-defuser has stumbled upon an active bomb. He opens it up, and finds the red and green wires conveniently located for him to cut. Being a seasoned member of the bomb-squad, Bob quickly determines that it is the green wire that he should cut, and puts his wirecutters on the green wire. But just before he starts to cut, the bomb starts to count down, ticking every second. Each time the bomb ticks, starting at time t=15t=15 seconds, Bob panics and has a certain chance to move his wirecutters to the other wire. However, he is a rational man even when panicking, and has a 12t2\frac{1}{2 t^{2}} chance of switching wires at time tt, regardless of which wire he is about to cut. When the bomb ticks at t=1t=1, Bob cuts whatever wire his wirecutters are on, without switching wires. What is the probability that Bob cuts the green wire?
Plain-text mathematical notation (without MathML)
Bob the bomb-defuser has stumbled upon an active bomb. He opens it up, and finds the red and green wires conveniently located for him to cut. Being a seasoned member of the bomb-squad, Bob quickly determines that it is the green wire that he should cut, and puts his wirecutters on the green wire. But just before he starts to cut, the bomb starts to count down, ticking every second. Each time the bomb ticks, starting at time t=15 seconds, Bob panics and has a certain chance to move his wirecutters to the other wire. However, he is a rational man even when panicking, and has a (1)/(2t²) chance of switching wires at time t, regardless of which wire he is about to cut. When the bomb ticks at t=1, Bob cuts whatever wire his wirecutters are on, without switching wires. What is the probability that Bob cuts the green wire?
Original LaTeX notation
Bob the bomb-defuser has stumbled upon an active bomb. He opens it up, and finds the red and green wires conveniently located for him to cut. Being a seasoned member of the bomb-squad, Bob quickly determines that it is the green wire that he should cut, and puts his wirecutters on the green wire. But just before he starts to cut, the bomb starts to count down, ticking every second. Each time the bomb ticks, starting at time $t=15$ seconds, Bob panics and has a certain chance to move his wirecutters to the other wire. However, he is a rational man even when panicking, and has a $\frac{1}{2 t^{2}}$ chance of switching wires at time $t$, regardless of which wire he is about to cut. When the bomb ticks at $t=1$, Bob cuts whatever wire his wirecutters are on, without switching wires. What is the probability that Bob cuts the green wire?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
6cebd424-8ffd-528a-b5c0-baa2cd0a7735
task_key
test--6cebd424-8ffd-528a-b5c0-baa2cd0a7735
task_revision_id
1
config / split
/ test

Official source

initial import