2.A classroom is composed of 10 students: 5 men and 5 women. The students are assigned intopairs at random, and each pair is assigned to complete a different task (T1, T2, T3, T4, T5).(a) How many possible configurations for the pair assignments exist? (Note: each configuration consistsof pairs and tasks assignments for all students).(b) What is the probability that all pairs consist of different-gender members?(c) If student A and B are friends, what is the probability that they are assigned to the same task together?

Let us denote men as M1,M2,M3,M4,M5 and women as W1,W2,W3,W4,W5Possible combinations are…

Answered: 2. A classroom is composed of 10…

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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TF.2
What is the class mark for a class interval of 19.50—22.50?
I need help with A, B, C. Three friends (A, B, and C) will participate in a round-robin tournament in which each one plays both of the others. Suppose that P(A beats B) = 0.2P(A beats C) = 0.4P(B beats C) = 0.7 and that the outcomes of the three matches are independent of one another. (a) What is the probability that A wins both her matches and that B beats C? and What is the probability that A wins both her matches? (b) What is the probability that A loses both her matches? (c) What is the probability that each person wins one match? (Hint: There are two different ways for this to happen.)
Fred has 4 place settings consisting of a dinner plate, a salad plate, and a bowl. Each setting is a different color. If Fred randomly selects a dinner plate, a salad plate, and a bowl, what is the probability that they all have different colors? The probability is
A couple has 3 children. Write out the sample space of genders for their children in order of birth, and find the probability that they have exactly 2 boys. (Assume that boys and girls are equallylikely.)
3. Two coins are tossed 700 times, and the results are Two heads: 205 times One head: 325 times No head: 170 times Find the probability of each event to occur? 4. If P(A)-7/13, P(B)-9/13 and P(ANB)-4/13, evaluate P(A/B)? 5. Two dice are rolled, find the probability that the sum of the number of both the dice is: A.Equal to 2 B.Equal to 5 C.Less than 12 6. Let X be the number of Tell in four tosses of a fair coin a) Construct the Probability mass function (pf) of X. b) Find the mean number of Tell and the variance c) Find P(0 2. (i)Determine the corresponding p.d.f. (f(x)). (ii) Determine the constant c. 8. If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value 9.Find the probability of getting at least 5 times head-on tossing an unbiased coin for 6 times by using the binomial distribution
The contents of urns, I, II and III are as follows: 1 white, 2 black and 3 red balls; 2 white, 1 black and 1 red balls, and 4 white, 5 black and 3 red balls One urn is chosen at random and two balls drawn from it. They happen to be white and red. What is the probability that they come from urns I II or III
a). A girl is randomly picking flowers in a meadow for a bouquet. She will stop once she has picked 4 dandelions. Suppose that a randomly selected flower is a dandelion with probability 0.70. Find the probability that her bouquet will have exactly 8 flowers in total. b). An entomologist has a collection of 20 insect specimens: 5 are butterflies and 15 are moths. He randomly selects a sample of 6 specimens to study. Find the probability that the sample contains an equal number of butterflies and moths. 2
A platter contains 48 doughnuts: 26 cake, 13 glazed, and nine jelly-filled. Suppose two doughnuts are randomly selected in succession without replacement. Find the probability (to 4 decimal places) of selecting two cake doughnuts. A. 0.0691 B. 0.2881 C. 0.2934 D. 0.5417
A man wants to adopt a puppy from an animal shelter. At the shelter, he finds eight puppies that he likes, a male and female puppy from each of the four breeds of terrier, briard, dachshund, and maltese. The puppies are each so cute that he cannot make up his mind, so he decides to pick the dog randomly. Find the probability that the man chooses a male puppy. The probability of choosing a male puppy is (Type a simplified fraction.) ...
In a lottery, the top cash prize was $659 million, going to three lucky winners. Players pick five different numbers from 1 to 57 and one number from 1 to 42. A player wins a minimum award of $450 by correctly matching three numbers drawn from the white balls (1 through 57) and matching the number on the gold ball (1 through 42) What is the probability of winning the minimum award? The probability of winning the minimum award is (Type an integer or a simplified fraction.)
. A swimmer, Sarah, hopes to compete in an upcoming meet. There are 8 team members eligible for the breaststroke event at the meet, but only 1 team member will be randomly selected to compete in that event. There are 4 team members eligible for the butterfly event at the meet, but only 1 team member will be randomly selected to compete in that event. Sarah is eligible to compete in both events. What is her chance of being selected for at least one of the two events? Select one: a. 1 in 4 b. 1 in 8 c. 3 in 8 d. 3 in 12

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