A Canada-USA committee is to be formed by choosing 10 people from 25 possible applicants. a)...

A Canada-USA committee is to be formed by choosing 10 people from 25 possible applicants.

a) How many committees are possible?

b) If 10 applicants are Canadian and 15 are American, how many committees have equal representation?

c) Two brothers, both from Canada, are on the committee. How many committees will have equal representation?

Clearly label each part and show your work.

Expert Solution

Calculating committees possible based on conditions given by combinations.

orchestra answered 2 years ago

Suppose an undergraduate-admissions committee rated 400 applicants and randomly chose 12 from those in the top...

Suppose an undergraduate-admissions committee rated 400 applicants and randomly chose 12 from those in the top 15 %. (i) Compute the probability that a person will be admitted given that he/she has the highest faculty rating among the 400 students. (ii) Compute the probability that a person will be admitted given that he/she has the lowest faculty rating. (b) In a production line, suppose 3 % of the products have Type A defects and 2 % of products have Type...

Each week, a subcommittee of four individuals is formed from among the members of a committee...

Each week, a subcommittee of four individuals is formed from among the members of a committee comprising seven individuals. Two subcommittee members are then assigned to lead the subcommittee, one as chair and the other as secretary. Calculate the maximum number of consecutive weeks that can elapse without having the subcommittee contain four individuals who have previously served together with the same subcommittee chair. The answer is 140. Could you explain why? Thank you so much!

A large study of DNA from people in the USA determined that the frequency for the...

A large study of DNA from people in the USA determined that the frequency for the recessive allele for ear shape .2 and the dominant is .8. If 10 % of the population shows the recessive phenotype is the population in HW equilibrium for this trait? Note that the population of the USA is over 200 million! no yes cannot be determined from the data given

A committee will be formed with 4 managers and 3 engineers selected randomly without replacement from...

A committee will be formed with 4 managers and 3 engineers selected randomly without replacement from 11 managers and 16 engineers. What is the conditional probability that engineer Al is on the committee given that engineer Jane is on the committee? Round your answer to three decimal places (e.g. 98.765). Would the answer be ((3/16)x(2/15))/(3/16) ---> (2/15) ----> .1333333

6. [11 marks] A special committee of five professionals is formed from a group of four...

6. [11 marks] A special committee of five professionals is formed from a group of four lawyers, three doctors and three teachers. At least three lawyers are needed in the special committee. Define X as the number of teachers in the special committee. Construct the probability distribution of the random variable X. Calculate the expected of X and provide an interpretation of it. Calculate the standard deviation of X.

A special committee of five professionals is formed from a group of four lawyers, three doctors...

A special committee of five professionals is formed from a group of four lawyers, three doctors and three teachers. At least three lawyers are needed in the special committee. Define X as the number of teachers in the special committee. a) Construct the probability distribution of the random variable X. b) Calculate the expected of X and provide an interpretation of it. c) Calculate the standard deviation of X

The grades of a sample of 10 applicants, selected at random from a large population, are...

The grades of a sample of 10 applicants, selected at random from a large population, are 71, 86, 75, 63, 92, 70, 81, 59, 80, and 90. Compute the sample variance. Can we infer at the 90% confidence that the population variance is significantly less than 100? (i.e. Perform Hypothesis testing)

Consider an economy consisting of 11 people, 10 citizens and their mayor. the mayor is choosing...

Consider an economy consisting of 11 people, 10 citizens and their mayor. the mayor is choosing whether to implement a sales tax, t, on the good x1 or an income tax, r, on each citizens salary. Suppose each good x1 and x2 has the common respective price of 1. Furthermore, each citizen receives an income of $10,000 and all citizens have the same utility preferences given by: U (x1, x2 ) = √x1 √x2 What is the budget constraint in...

Suppose that a committee of 12 people is selected in a random manner from a group...

Suppose that a committee of 12 people is selected in a random manner from a group of 100 people. Determine the probability that two particular people A and B will both be selected.

A school dance committee of 4 people is selected at random from a group of 6...

A school dance committee of 4 people is selected at random from a group of 6 ninth graders, 11 eighth graders, and 10 seventh graders. What is the probability that the committee has all seventh graders?

Question