committee of five to study transportation issues will be randomly selected.a. If one person on the council is chosen at random to draw the names out of a hat,what is the probability that the person drawing the names is a Democrat?b. How many ways can the committee be formed if there are no restrictions oncomposition?C. How many ways can 3 Republicans be chosen?23. A city council consists of ten members. Four are Democrats and six are Republicans. Ad. How many ways can 2 Democrats be chosen?e. What is the probability that the random selection of the five-person committee willresult in 3 Republicans and 2 Democrats?

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A group consists of four Democrats and five Republicans. Four people are selected to attend a conference. a. In how many ways can four people be selected from this group of nine? b. In how many ways can four Republicans be selected from the five Republicans? c. Find the probability that the selected group will consist of all Republicans.
Please show your solution in step by step process.
Nine people apply for three jobs. Five of them are women, four of them are men. 1. If three people selected at random, what is a probability that all three are woman?(Give your answer as a fraction, you do not need to simplify) 2.lf three people selected at random, what is a probability that only one is woman?(Give your answer as a fraction, you do not need to simplify) 3. If three people selected at random, what is a probability that at least two are men?(Give your answer as a fraction, you do not need to simplify) 4.lf three people selected at random, what is a probability that at most one is a man?(Give your answer as a fraction, you do not need to simplify)
A Statistics instructor wishes to know the average age (in month) of his 200 students. He decides to choose 25 students from the class and ask them for their age. All 200 names are put in a hat and 25 names are then chosen at random (without replacement). The average age of the students chosen is observed to be 231 months. The group of 25 students is known as what?
Consider a political discussion group consisting of 4 Democrats, 9 Republicans, and 6 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting two Democrats.
A student-faculty government committee of 4 people is to be formed from 20 student volunteers and 5 faculty volunteers. a. If one person from the group of volunteers is chosen at random to draw the names out of a hat, what is the probability that the person drawing the names is a student? b.How many ways can the committee of four be formed if there are no restrictions on composition. c. How many ways can two of the students be chosen? d. How many ways can 2 faculty be chosen? e. What is the probability that the random selection of the four-person committee will result in two students and two faculty?
There four foreign nationals in a group of fifteen people. Four people are chosen at random. a. Calculate the probability that there is one foreign national among the chosen four рeople. b. Calculate the probability that all of the chosen people are foreign nationals. c. Calculate the probability that none of the chosen people are foreign nationals.
A group consists of five men and six women. Five people are selected to attend a conference. a. In how many ways can five people be selected from this group of eleven? b. In how many ways can five women be selected from the six women? c. Find the probability that the selected group will consist of all women. a. The number of ways to select five people from the group of eleven is b. The number of ways to select five women from the group of six women is c. The probability is. (Type an integer or a simplified fraction.) G
8. The composition of the 108th Congress is 50 Republicans, 48 Democrats, and 2 Independent. A committee on aid to higher education is to be formed with 3 Senators to be chosen at random to head the committee. Find the probability that the group of 3 consists of a. All Democrats b. One Democrat, one Republican, and one Independent
nuclear power station is to be built on one of 20 possible sites. A team of engineers is commissioned to examine the sites and rank the three most favourable in order. In how many ways can this be done? a. 4840 O b. 9640 3686 6840 O O C. d. O
17. A city council consists of ten members. Four are Democrats and six are Republicans. A a. If one person on the council is chosen at random to draw the names out of a hat, committee of five to study transportation issues will be randomly selected. b. How many ways can the committee be formed if there are no restrictions on what is the probability that the person drawing the names is a Democrat? composition? C. How many ways can 3 Republicans be chosen? d. How many ways can 2 Democrats be chosen? e. What is the probability that the random selection of the five-person committee will result in 3 Republicans and 2 Democrats?

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