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
A. From a lot of 12 flares, 4 are selected at random. If the lot contains 4 defective flares, what is the probability that all 4 will not work?
B. What is the probability that at most 2 will not work?
Thank you for your help
Answer Sorry for my delay!
A. From a lot of 12 flares, 4 are selected at random. If the lot contains 4 defective flares, what is the probability that all 4 will not work?
Follow hypergeometric distribution, P(all 4 will not work)= (4-combinations from 4 elements * 0-combinations from 8 elements)/(4-combination from 12 elements)
In general, P(x will not work) = (x-combinations from 4 elements * (4-x)-combinations from (12-4) elements)/ (4-combination from 12 elements)
Where x-combinations from 4 elements = 4!/(x!(4-x)!) , which can also be read as 4 choose x.
B. What is the probability that at most 2 will not work?
Follow hypergeometric distribution, P(at most 2 will not work)=P(0 will not work)+P(1 will not work)+P(2 will not work)
