About Vivian Expertise I can answer questions on probability, distributions, statistical inference, statistical estimation, hypothesis testing, analysis of categorical data, linear regression, generalized linear regression, ANOVA, and linear mixed models. I cannot answer questions on stochastic processes.
Experience I have worked as a research assistant at the University of Michigan, Ann Arbor for two years.
Organizations American Statistical Association
Education/Credentials University of Michigan, Ann Arbor
Master of Science
Question QUESTION: I have 35 consecutive numbers. I randomly chose any 5 numbers, no two numbers being the same. What is the probability that another 5 random numbers (none of those being the same) are equal to any of the original 5 numbers? Note: The original 5 is put back into the 35 population. I need to see the math. Thank you.
ANSWER: The probability that at least one of another 5 random numbers (none of those being the same) exits in the original 5 numbers = 1- probability that none of the second 5 random numbers are equal to any of the original 5 numbers = 1- the number of 5-combinations from 35 elements =1- the number of 5-combinations from 30 elements/ the number of 5-combinations from 35 elements=1-0.44=0.45
The number of different sets of 5 random numbers out of 35 consecutive numbers is the number of 5-combinations from 35 elements.
The number of the sample space, i.e. the number of different ways to choose two sets of 5 random numbers by your rule = (the number of 5-combinations from 35 elements) ^2
The number of different ways to choose two sets of 5 random numbers so that none of the second 5 random numbers are equal to any of the original 5 numbers is [ the number of 5-combinations from 35 elements * the number of 5-combinations from 30 elements].
Does it make sense? Please feel free to give me your thoughts. Thanks!
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QUESTION: Thank you for your timely response. I understand that the answer to my question is 1-0.44=0.45,but I did not understand the reasoning. My problem is the definition of "=1-the number of 5-combinations from 30 elements/the number 0f 5-combinations from 35 elements=1.044..." I cannot get the answer 0.45. I'm sorry.
Answer Sorry. I mean 1-0.44=0.56.
It is 1-the number of 5-combinations from 35 elements*the number of 5-combinations from 30 elements/ (the number of 5-combinations from 35 elements)^2=1-the number of 5-combinations from 30 elements/ the number of 5-combinations from 35 elements.
