benchmarks.wiki / Public workspace
..······.......···········...........···:::::::::::::::···········::::::::::::::::::::::----=========--:::::·······.
........ ..............······::::::::·······························:::---:::::::::::------::::·····........
........·········............................. .···--------::::::············............
..··---------:::·······.........
..··--=====---::···..........
..··-===++===--:··....
..·:==++++++==-::·...
..·:=++*****++=-:··..
...·:=+**####*++=-:·... ..
..········... ........ . ...··:::::::···......··:=+*##%%##*+=--:·... ..........
..··::::::··. ..·::::::··... ..·:-==+*****+==-::······-=+*#%%%%%#*+=-:··........·······...
..··::::··. .·:-=+**++=-:··......·:-+*%@@@@@@@%*+=-:::::--=+*#%@@@@%#*+=-:··....···:::---::··..
..... ............······::::::---::::::::::················::::::::::::::::--==++*###%%###**++===++****+=-:·.
......····::::::::::::::····················..........·····::::::::---==+++*****+++==---==+++===-:·.
.........············....... ............... ···::::::::::---=========---::::-------:·.
.··::::::::::::::-------::::····:::::::··.
.··:::::::········::::::·····...········..
.··----:::··············.................
..··-----::···..............
..·:====--::··....
...::=====--::·...
...····... ......... ...···::::::···..........:::+++++==-:··..
..······.. .··::--:::··.. ..·::-=+******++=-::······:::+*****+==-:··.. ........
..····.. .·:-=+**++=-::·....··:-+*%@@@@@@@@%#*+=--::--==+**####*++=-:·... ....·······....
.....····::::----------::::::::·················:::::-----:::::---=++*#%@@@@@@@@@%##*****##%@@%#*+=-:·.
......····::::--------:::·····.........................··········:---==+**#%@@@@@@@%%#***++**#%@@%#*+=-:·.
.............·············..... ...... ....···::--==++*##%%@@%%##**++++++*#%@%#*+=-:·
..··:::---==++**#####**++======++*##**+=-·.
··:::::---==+++++++++==-------=++++==-:·.
··::::::::----=====---:::::::::-----::·..
··:::·····::::::::::::··········:::···..
..··:::·················.................
...··:::····............... ......
....... ....·..... . ...··········.... ...···-:::··....
...··.. ..·::----::··........·:--=++***++=--:··......····::=---::··.. .........
...··.. .·-=+****+=-::··..··:-=+#%@@@@@@@%#*+=-::··:::--=======-::·.. ......····.......
....····:::-----==------:::::::::··············:::---=======------==+*#%@@@@@@@@@@@%#*++=++**#@@@@@%#*+=:·.
.....·······::::--------:::····......................·····::::::::··:::=+*#%@@@@@@@@@@@%#**++++*#%@@@@@%#*+=:·.
..............············..... .............:::++*#%@@@@@@@@@@%##*+++**#%%@@@@%#*+=:·.
...::=+*##%@@@@@@@@@%#**++++**#%%@@@%#*+-:..
..·:==+**#%%@@@@@%%#**++===+++*##%%#*+=:·.
..··-==++**#######**++==----===++**++=-:·.
..··----==+++++++++==--:::::::---==--::·..
..··:::::-----------::··········:::::··...
··:·······:::::·····..........·······...
..... ...····.... .......·...... ··.·····.........................····....
....... .·::-----::··.. ..··::--===--::··.... .....······:···.... .............·····....
...... .·:-++****+=-:··....··:-=+*##%%##*+=-:···....···::-----::··... ....··············....
...·····:::-----===--------:::::::::::::···::::--==++*****++==------==+*#%@@@@@@@%#*+=-::::--=*#%@@@@@@%#+-:..
....·······:::::-----::::·······....··.........····:::--------:::::::::--#%@@@@@@@@@%#*+==---==+*%@@@@@@@%#+-·.
..............········...... .....................-==%@@@@@@@@@@%#*++===++*#%@@@@@@@%*=:·.
..·==%@@@@@@@@@@@%#*++++++**#%@@@@@@#+-:·.
.·-=%@@@@@@@@@@@%#*++===++**##%%%%#*=:·.
..--#%%@@@@@@@%%#*++=======+++****+=-:·.
..:-**##%%%%%##**+==---:::---======-:··..
..::=++++***+++==--:::·····::::----:::··..
...··-----------:::············::::::::···..
... ....····.... . ..... .....···::··············.....······::::::::···.
...... ..·::-----::·.. ...····:····... .....······..···..............··········::::::::···..
...... .·:-=+***++=-:·.. .··:--=====--::·.... ....··::::::::··... ....··::::::::::::::····....
....··::::---------------==========-----::---==+**##%%##*+=--:·····::-=+*##%%##*+=-:·.....·:-=*#%@@@@@@%#+-·..
.....·····::::::::::::::·····:::::::··········::---=======--::·······::-==%@@@@%%#*+=-::··::-=+*%@@@@@@@%*=:·.
...............................................··········..........··=++@@@@@@%#*+==-----=+*#%@@@@@@%#+-·.
···+*@@@@@@@@%#*+==-===++*#%%%%%#*+=:·.
··+*@@@@@@@@%#*++======++***#***+=-:..
··+*@@@@@@@@%#*+==------===++++==--:·..
··=+@@@@@%%##*+==--:::::-----===---::···..
··-=#####**++==--:::···:::::----====--::··.
...::======----:::·······::::----======--:·.
........... . ...........···::::::···········:::::::-----====--::·.
...... ..··::---::··.. ........... .....·········...··........····:::::-----::::::::::::··..
...... .·:-==+++==-:·.. ..··::::::··... ....··:::::::::··... ...··::---===---::···..........
..··::---------=====++***####**++==------==+*###%##**+-:·.. .·:-==++++==-:·.. ..·:=+#%@@@@@@%*+=:·.
....···::::::::::::::------------::::::::::--===++===-::·... ..··:--==##**+=-:··...··:-+*#%@@@@@%*+=:·
........................··...............··········.... ...···+++@%%#*+=-::::::-=+*##%%%%#*+-:·.
·::**@@@%#*+==------==++*****+=-:·.
::**@@@@%#*+==-------===+++==--:··..
::**@@@@%#*+==--:::::----====----:::·····..
·:++@@%##*+==--::::::::----======++===--:·..
··==#**++==--:::::::::----===+++**#**+=--:·.
...::===----:::::::::-----====++++***++=-:·.
........... . ..................···:::::::::::------------------===--::·..
...···:::::··... ........... ......·············..........···::--======---::·············..
.... ..··:--===--::·. ..·······..... ....··:::-----:::··... ..··:--===+===-::·.. .......
..·::------====++**#%%%@@%%##*+=--::::--==+*****++=:·. ..·:-====--:·.. ..·-=+#%@@@@@%#+=:·.
..···:::::::::---===++++++==--:::·····::---====--::·.. .··::-----+=-:··....··:-=+*#%%%%#*+-:.
.............···············...........·········... ...·····===*+=-::····::-==+****++=-:·.
:::++#*++=-:::::::--======--:··. ..
::*+%#*+=--:::·::::---------::::··::::::··.
::++%#*+=--:::··::::----=======+++*+++=--:·.
··==**+==--:::::::---===+++***###%%%#*+=-:.
··--+==------------====++++***###%%#*+=-:·.
...:·---------=================++++++=-::·.
............ . ....................... ...·::::--===++++===--:::·····:::-:::··.
...···::::···... .....................·····::::::····..... ...··::-==++++==-::·.. ..·····...
..·:::-----::·.. ...·······..........··::---====--::··.. ..··:--==+++=--:·. .··:::··.
.··:::-----==++*##%%@@%%#*+=-:··...··::-==++++=-:·. .·:-====--:··.. ..·:-=+*#%@%%#*+-:.
..···:::::::--===+++++++=--:···....···::------:··. ..·::------::::··...··::-=++***+=-:·.
..........······:::::····.............······.... ...·······--:-::······::---==---:··. ..···.
···--=-::·······::::--:::::·······::-----:··.
··--=-::········:::----======+++**#**++=-:·.
··--=--:::::::::--===+++***##%%%@@@%#*+-:·.
·.-:=---------====+++****###%%%@@@@#*+-:·.
..::=======+++++++++++++++++*******+=-:·.
...··--==++++**+++==---:::::::---===-::·.
.............. .......... · ....................... ..·:--==++++++==-:··.. ...··::-::··.
...··:::::···... .......................···:::::::::···... .·::-==++++=--:·. .·::---:··.
..·::----::··.. ..·········........···:--==+++==--:·.. .··:-==++==-::·. ..·:-===--:·.
...····:::-==+*#####*+=-:·.. ..·:-=====--:·. .·:-==+++==-::··.....·::-=+****+=-:·. ......
.....···:::--===+===--:··.. ..··::::-::··.. ..·::------::··.·.....··::------:··. .··::::·.
.......············.... .....··..... ...········..··.·.......···:::::····.....··::-=====--:·.
...·.·.......··::::------====++**##%#*+=-:·.
..··:······:::--==+++***###%%%@@@@@%*+=:·..
..:·-------===+++****###%%%@@@@@@%%*+-:·..
..::==+++++******+++++****#######**=-:·.
..::++********++==--------===++++==-:·.
...::++*****++=--:··......··::---==-:··.
....····............................ · .........·····...... .··-=+++++==-:·.. ..·:--===-:·..
..··::::::··.... ......·····...........···:::-----:::·... .·:-==++==-:··. .·:-==++=-:·.
..··::---::·.. ..··::::::::···.....··::-==+++++=-:··. .·:-=+++++=-:·. .·:-=+***+=-:·.
..·::-=+++++=-:·.. .·:--====--:·. .·:-=+***++=--:··.....···::----::·.. .·:--==--:·.
..··::-------:··.. ..··::::::··.. .··:--===--::··.. ...·········.........·::-=+**++=-:·.
....·······.... ........... ....·······.... ...···:::::-------==+++**####*+=-:·.
....···:::--===+++***###%%%%%%%%#*+=::·.
..··:----==++++***####%%%@@@@@%%##*=-:·..
..:-+++***************###%%%%##**+=-:·..
··-=#####***++====--===+++*****+==-:·.
.·-=####**+=--:·······::--==+++==-:·..
...--***++=--:·.. .··:--=====-:·..
.....···........ ............ .·.....········.... ·::++++=--:·. .·::-==++==-:·.
..··::::···.. ...···········.......···::------::··. .··==+++==-:·. .·:-==++++==:·.
..··:::··. .··:--=====--::··....··::--=====-::·. .·:=+*****+=-:·. .·:-=++***+=-·..
.·:--===--:·.. .·:-==++==-:·. .·:-=+*****+=-::·.. ...·······.... ..··:-=++***+=-:··.
..·:::::::··.. ..··::::::··.. ..·::------::··.. ...···::::::::::---==+++*****+==-:·.
....····.... ........... .....···...... .···::---===++++*****######***+=-:··..
··---===++++***####%%%%%%%##**+==-:··..
..--+*************####%%%%%##*++=-:··...
··==###***+++=====++***####**++=-::·...
··==##**+==-::::::--==++****++=--:·...
··==**+=--:·......··:--=++++++=-::·..
..·--++=-:··. .·:--=+++++=--:·..
.......... ....................:..·······.... ...---++=-:·. .·:-=+++++==-:·.
...··.... ..··::::-::::···......····:::::::·.. ..·::--**++=-·.. .·:-=+++++==-:·.
...... .·:-=+**##**+=-:·.. ...··::---::··. .·:-=**####*+-:·. .·:-=+++*++=-:·.
.·:--==--:·.. ..·:-==+++=-::·. ..·:-=++**++=--:·. ...············::::--==++++++++=-:··.
.··::::···.. ..··:::::::··.. ..··::::::::··... .··:::----======+++++++++++++===-:··..
.......... ........... ............. ···--====++++*****#####***+++==--::··...
...--++++++++****#########**++=--::··.....
··==***+++++++++**#######**+=--::··.......
··==*++==------==++**####**+=--:···........
··=-+==-::····::--=+**###**+=--:···........
··--=-::·......··:-=+******+=--:···........
···-:=-:·.. ..·:-=+*****+=--:··.........
.....·····....... ....:........ ...···---=-:·. .·:-=++****+=-::·..........
.··:--======-::·... ...·······.. .··:--===-+=-:·. .·:-=+****+=-:··... ......
.:-=*#%@@@%#*+-:·. .··::--::··. .·:-=+*#####*+-:·. .·:-=++**++=-:·.. ....
..·:----:·.. .·::-=++++==-:·.. ..·::-=====--::·.. ...···::::-----------============---:·..
..··:::··.. ...··:::::::··... ...···::::····............···----======+++++++++++===---::::··...
......... ........... ..........................:::====+++++*********++==--:::····....
···--++===++++***#####**++=--:····.......
··--+=======++***#####*++=--:····.·.......
··-:=--:::---=++*######*+==-:···········...
··::-::····::-=+**#####**+=-::············.
·.:·:··....··:-=+*##%%##*+=-::·····:::::··.
··.:·:·.. ..··:-=+*##%##*+=--:····:::::::··.
...··········... ..·..... ...·······::··.. .·:-=+*#####*+=--:····::::-:::·.
.·:-==++**++=-:·. ..·····... ..·:--=====-:::·. .·:-=+*####*+=-::·····:::--::·.
.·:-+*#%@@@%#*+-:. .··:--==--:··. ..·:-=+*#####*+-:·. .·:-=+*****+=-:···.···::::::·.
.··:::::·.. ..·:--==++==--:·.. ..··:::----:::···.........····::::-------------------------::::··..
..······... ....···::::···.... ....····························:---===============---::::·····...
......... ......... ................................:::======+++++++++==--:::···.......
...::--====+++*****++==-::···.........
..::----==++***##***+=--:··............
..··:::--==+**#####**+=-::··.....····....
..··:::::-=++*##%%##*++=-:··············..
..·.····::-=+*#%%%%%#*+=-::······::::::··..
...·.·..··:-=+*#%%%%%##*+=-::····::-----:··.
...··:::::::··.. ..·.. ..·········..·.......·:-=+*#%%@%%#*+=-:::··::-====--:·.
.··:-==++*++==-:·. ..·······.. .··:-==++===-:··... ..·:-+*#%%%%%#*+=--:::::--==+==--:.
...··:-=++*####*+=:·. .·:-=+++==-:··.. ..·:-=+*#%%##*+=:·.. ..·-=+*#%%%%#*+=-:::·::--=++++=-:·.
..···:···.......··::-------::··.. ...···::::::::::·············::::::::-------------------------:::···...
..······.............····...............···································---------------:::::::······....
....... ...........................................···---========---:::·····.......
...··--====++++===--::··........
..··--===+++*+++==-::··....
..··--==++******+==-:··.... ...
..··:--=+**####**+=--:··.............
..··:--=+*##%%%##*+=-::·........···....
.. ..::-=+*#%%%%%%#*+=-:··.....····:···..
..··::::::···.. .....· ..···::::····... ...·:-=+*#%%@@@%#*+=-::·······:::--::··.
...·:--=====--:·. .··::::···.. ..·:-==+++++==-:··...···:-=+#%%@@@@%#*+=-::····:::-===--:··.
.....·::--====--:·. ·:-=+++++=-:··.. ..··:=+*#%@@%%#*+=-:·....·::=+*#%@@@@%#*+=--::··::--=++++=-:·..
███╗ ███╗███╗ ███╗██╗ ██╗ ██╗ ██████╗ ██████╗ ██████╗
████╗ ████║████╗ ████║██║ ██║ ██║ ██╔══██╗██╔══██╗██╔═══██╗
██╔████╔██║██╔████╔██║██║ ██║ ██║█████╗██████╔╝██████╔╝██║ ██║
██║╚██╔╝██║██║╚██╔╝██║██║ ██║ ██║╚════╝██╔═══╝ ██╔══██╗██║ ██║
██║ ╚═╝ ██║██║ ╚═╝ ██║███████╗╚██████╔╝ ██║ ██║ ██║╚██████╔╝
╚═╝ ╚═╝╚═╝ ╚═╝╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ $ open /benchmarks/mmlu-pro/tasks/default--test--7757▌ posts · files
MMLU-Pro / 7757 / Suppose a fair coin is tossed 50 times. The bound on the probability that the…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
question
Suppose a fair coin is tossed 50 times. The bound on the probability that the number of heads will be greater than 35 or less than 15 can be found using Chebyshev's Inequality. What is the upper bound of the probability?
category
math
options
- 0.075
- 0.250
- 0.150
- 0.175
- 0.100
- 0.225
- 0.125
- 0.050
- 0.300
- 0.200
src
theoremQA-Math
Discussion
No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. 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. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.
Source and history
- upstream_id / Original problem ID
- 7757
- task_id
32820ae2-7ec6-5ea4-a91c-975274060a9c- task_key
default--test--7757- task_revision_id
- 1
- config / split
- default / test
initial import