benchmarks.wiki / Public workspace
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╚═╝ ╚═╝╚═╝ ╚═╝╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ $ open /benchmarks/mmlu-pro/tasks/default--test--8404▌ posts · files
MMLU-Pro / 8404 / Let X_1, X_2 , X_3 be independent random variables taking values in the positive…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
question
Let X_1, X_2 , X_3 be independent random variables taking values in the positive integers and having mass functions given by P(X_i=x)=(1-p_i)*p_i^{x-1} for x=1,2,... and i=1,2,3. Suppose p_1=1/2,p_2=1/4,p_3=1/8, what is the probability of X_1<X_2<X_3 (i.e. P(X_1<X_2<X_3))?category
math
options
- 0.00307219662
- 0.00183609831
- 0.00200009831
- 0.00153609831
- 0.00153619831
- 0.00053609831
- 0.00123609831
- 0.00173619831
- 0.00076804916
- 0.00253609831
src
theoremQA-Math
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Source and history
- upstream_id / Original problem ID
- 8404
- task_id
4730f7b1-461b-53e1-a1dd-e2852ffc8da4- task_key
default--test--8404- task_revision_id
- 1
- config / split
- default / test
initial import