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 A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves 6 times, what's the probability she gets
a.) all 6 serves in?
b.)exactly 4 serves in?
c.)at least 4 serves in?
d.)no more than 4 serves in?
alright so I understand combinations and permutations but I have a really hard time trying to use it in a problem like this.
Answer Can I say that the probability that the player makes a successful trial is 0.7? The reason for me to ask this question is that it is said that the player makes a successful FIRST serve 70% of the time. Does the word first here matter?
If we can say that the probability that the player makes a successful trial is 0.7. The total number of serves in out of the 6 times has the binomial distribution.
Probability that 6 out of 6 is the binomial coefficient 6 choose 6* 0.7^6*(1-0.7) ^0= 0.117649. You may obtain it by BINOMDIST(6,6,0.7,FALSE) in microsoft excel.
Probability that 4 out of 6 is the binomial coefficient 6 choose 4* 0.7^4*(1-0.7) ^2= 0.324135
. You may obtain it by BINOMDIST(4,6,0.7,FALSE) in microsoft excel.
Probability that at least 4 out of 6 is 1- [the binomial coefficient 6 choose 3* 0.7^3*(1-0.7) ^3+the binomial coefficient 6 choose 2* 0.7^2*(1-0.7) ^4 +the binomial coefficient 6 choose 1* 0.7^1*(1-0.7) ^5 + the binomial coefficient 6 choose 0* 0.7^0*(1-0.7) ^6 ]= 0.74431. You may obtain it by 1-BINOMDIST(3,6,0.7,TRUE) in microsoft excel.
Probability that no more than 4 out of 6 is [ the binomial coefficient 6 choose 4* 0.7^4*(1-0.7) ^2+ the binomial coefficient 6 choose 3* 0.7^3*(1-0.7) ^3+the binomial coefficient 6 choose 2* 0.7^2*(1-0.7) ^4 +the binomial coefficient 6 choose 1* 0.7^1*(1-0.7) ^5 + the binomial coefficient 6 choose 0* 0.7^0*(1-0.7) ^6 ]= 0.579825. You may obtain it by BINOMDIST(4,6,0.7,TRUE) in microsoft excel.
Note: The binomial coefficient 6 choose 4 = 6!/[4!(6-4)!]
