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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

You are here: Experts > Science > Mathematics > Probability & Statistics > Probability

Probability & Statistics - Probability

Expert: Vivian - 5/23/2008

Question
A die is thrown 20 times and a success is defined as a one or a six on the upface of the die.

Use the binomial distribution to determine the probability of getting exactly five successes in the 20 trials.

Thank you very much for your help

Answer
The total number of success out of 20 trials has the binomial distribution with the probability of success 2/6. Probability of getting exactly five successes in the 20 trials is the binomial coefficient ‘20 choose 5’* 0.333^5*(1-0.333)^15= 0.15.

Note: the binomial coefficient ‘20 choose 5’is the number of 5-combinations from 20 elements. We have assumed that the 20 trials are independent and identical trials. ‘Identical trials’ means that the probability of hit is the same for each trial. ‘Independent trials’ means that the results of trials are independent random variable. .

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