1. List the elements in the sample space S ={x|x3 + 2x² – 5x – 6 = 0} .2. How many distinct permutations can be made from the letters of the word"miscellaneous" that start with “mis"?3. Ten people are gathered to form a committee of size 4. If there are 6 men and 4women in the group and one such woman is Ms. Cruz, what is the probability thatthe committee is composed of 3 men and Ms. Cruz?

We need to calculate the, 1. List the elements in the sample space S = {x|x³ + 2x² - 5x - 6 = 0} .…

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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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1. Suppose 1495 Valencia College students were selected at random from the entire student body and given an experimental H1N1 flu shot. All 1495 were exposed to the flu, but only 332 of them actually ended up sick with the flu. Let p represent the probability that the flu shot will be successful. (Read this carefully!) A. Find the point estimate for the population proportion from this study. Show your simplified fraction for the point estimate. Use proper notation. B. Build a 98% confidence interval for the real population proportion by hand using the formula. Draw a picture that represents the problem and clearly indicate your final answer C. Use a complete sentence or two to interpret your confidence interval.
4. In an organization consisting of 5 women and 10 men, a committee of four individuals is to be selected at random from the 15 people. Find the distribution of the random variable, X = Number of women on the committee. %3D
A bag contains 8 black, 7 yellow, and 10 green marbles. If a sample of 6 is drawn at random, how many samples are possible in which the marbles are: a. all green? b. 2 black, 2 yellow, and 2 green?
13. Heather is interested in determining the probability that a randomly selected card from a standard deck of 52 will be a club. She reasons that the deck contains clubs (C), spades (S) diamonds (D), and hearts (H). She constructs the sample space S = (C,S,D,H). Determine if the sample points are equally likely or not equally likely.
13.Imagine a population of balls in which all are red except for three green ones. If we randomly sample two balls, without replacement, and the probability of getting green both times is p=0.025, which of the following is the number of red balls in the population?
2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:
2. Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of 56 students were asked on which night of the week they did the most homework. The results were distributed as in the table below. Number of Students Sunday Monday Tuesday Wednesday Thursday Friday 11 5 8 10 7 10 Saturday 5 From the population of students, do the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week? What type of hypothesis test should you use? (You must justify your answer with a complete hypothesis test and an explanation, within context, using complete sentences.)
. List the 10 possible samples (without replacement) of size 2 that can be obtained from the population of five officials. Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Representative (R) Press Secretary (P) b. If a simple random sampling procedure is used to obtain a sample of two officials, what are the chances that it is the first sample on your list in part (a)? the secondsample? the tenth sample?
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1.) A basket contains 11 red apples and 8 green apples. A sample of 5 apples is drawn. Find the probability that the sample contains the following, and give your answer as a reduced fraction. (a) All green apples (b) 2 green apples and 3 red apples (c) More red than green apples

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