Probability problem:2: Out of 5 mathematicians and 7 statisticians,a committee consisting of 2 mathematiciansand 3 statisticians is to be formed. In how manyways can this be done if :(a) any mathematician and any statistician canbe included,(b) one particular statistician must be on thecommittee,(c) two particular mathematicians cannot be onthe committee?

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Answered: Probability problem: 2: Out of 5…

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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5. In a recent electrion, 72% of the voters voted to elect candidate Lopez for mayor. In the same election, 60% of the voters voted in favor of Proposition Q. 54% of the voters voted for both candidate Lopez and also voted in favor of Proposition Q. Find the propability that a randomly selected voter... a. ... voted for Lopez OR voted in favor of Proposition Q. b. ... voted for Lopez, given that they voted in favor of Proposition Q. c. ... didn't vote for Lopez nor did they vote for in favor of Proposition Q.
(3) Times, Wall Street Journal, and USA Today: In a survey of 150 business travelers, it was found that of three daily newspaper, New York 71 read New York Times; 43 read Wall Street Journal; 34 read USA Today; 30 read New York Times and Wall Street Journal; 25 read New York Times and USA Today; 15 read Wall Street Journal and USA Today; 10 read all three. A person is selected at random from this 150 travelers. (a). What is the probability that the randomly selected person reads New York Times or USA Today but not Wall Street Journal? (b). Given that this traveler read at least one of these three newspapers, what is the probability that he/she read USA Today? (c). Given that this traveler read exactly one of these three newspapers, what is the probability that he/she read Wall Street Journal?
After an earthquake, 32 homes in a remote area were checked by public safety officers before nightfall. They found that 22 of the houses had no gas, including 10 houses whose own gas lines were damaged. (A house loses its gas service if it has damage to its own line or if there is damage to the feeder line.) Of those houses that lost their gas, only 4 did not lose their electricity. Twenty-four houses in all had no electricity, the same number of them lost only their electricity as those that both lost electricity and had damage to their gas lines. How many of the houses checked did not lose either gas or electricity, and how many lost only their gas service! Students, draw anywhere on this slide!
16. A candidate is called for interview by the three companies. For the first company there are 12 candidates and for the there second are 15 candidates and for the third there are 10 candidates. What are the chances of his getting at least one of the companies.
Macrostates, Microstates, and Probabilities ) Macrostates and Microstates: 1) Suppose we flip n = 2 coins at the same time. If we are interested in how many heads we might get, then we can define a macrostate by just naming N = the number of heads. How many possible macrostates are there when you flip 2 coins? 2) Now we count the total number of different possible ways the coins can land when we toss two coins. We call these "possible ways" microstates. For our two coin toss, list all the possible microstates.
"Question 3 (MaC)". (i) John has 5 toy cars and 4 toy buses that are all different from each other. John arranges these 9 toys in a line. Find the number of possible arrangements if: (a) (a) the cars and buses are arranged alternately. (B) the buses are all next to each other. (b) John randomly chooses 4 toys to take on holiday with him. Find (a) in how many ways John can choose the 4 toys. (B) the probability that his choices will include both his favourite car and his favourite bus. | (ii) Consider the function f(x) = x" +1 (a) Evaluate lim x→® x* +1 (b) Find the stationary point of the curve y = f(x) and determine its nature. (c) Find the point(s) of inflection of the curve y = f(x). (d) Sketch the curve y = f(x) showing all the features found above. Using your graph, find all values of k for which the equation kx² = 1-k has exactly one solution. (e)
You are trying frantically to get dressed, and you need to reach into your sock drawer to get two matching socks in the dark. Your sock drawer contains 20 socks, consisting of 10 matched pairs. All of them are only black or white, and they are loose, disorganized randomly, and not bound together. This means you have 10 black and 10 white socks in your disorganized drawer. This makes 10 total matching pairs of 5 pairs of white and 5 pairs of black. 1. How can you guarantee success of picking a matching pair? In other words, what is the minimum number of socks needing to be picked to guarantee a matching pair? (Hint: There is a right answer to this question!) 2. Explain dependent and independent trials

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