1. RandomizationUse indicator random variables to solve thefollowing problem: Supposen customers turn ina garment for dry cleaning. While cleaning allthe clothes, the dry cleaner accidentally losesthe tickets and decides to randomly select agarment to give back to a customer. What is theexpected number of customers that get backtheir own clothes?Suppose you are given a biased coin whichlands heads with probability of 2/3. For anunbiased flip, you want two events with equalprobability. How can use the biased coin toproduce a fair flip (two events with equalprobability)? Describe the two events and showthat their probabilities are equal. [Hint: Considertwo consecutive flips of the biased coin.]

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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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12.) Jar 1 contains 2 orange marbles and 1 green marble. Jar 2 contains 1 orange marble and 2 green marbles. Jar 3 contains 1 orange marble and 1 green marble. Fist a jar will be selected, then one marble will be drawn from that jar. The probabilities of selecting the first, second, or third jar are 1/2, 1/3, and 1/6 respectively. A green marble is drawn. What is the probability that it came from Jar 2? This is a Bayes' Theorem problem.
A company in California has multiple employees working in different professions.In the company 10% of the males and 20% of the females have an salary of more than $5500. In this company, 60% of the employees are males. If an employee is selected at random and found to have a salary of more than $5500, find the probability that the employee is a male?
Suppose you have a large bucket of fruit candy, where 1% is orange flavor, 13% is mango flavor, 9% is apple flavor, and the rest is is grape flavor. You pick one candy at a time from the bucket, at random, without looking. What is the probability that you pick a mango candy before an orange one?
In the experiment of tossing a coin four times, what is the probability ofobtaining exactly 2 tails if it is known that the first and the last tosses are different?
2. A kindergarten class has 6 boys and 7 girls. At the end of each day, the teacher selects 5 students, uniformly at random, and asks them to help clean up the classroom. One of the boys in the class is named Vito. Show that, with probability = 38%, Vito and at least one girl will be amongst the 5 students asked to clean up today.
A biased coin has a 2/3 probability of landing heads and a 1/3 probability of landing tails.You toss the coin 9 times. Which of the two options below is more likely to happen?• The coin lands heads only 3 times, and lands tails 6 times.• The coin lands heads all 9 times.
7.) 1.You play a game with your friend where your probability of winning is 5%. If you play the game 50 times, What is the probability that you lose every game? What is the probability that you win the game at least once?
A couple plans to have four children. The father notes that the sample space for the number of girls the couple can have is 0, 1, 2, 3, and 4. He goes on to say that since there are five outcomes in the sample space, and since each child is eaually iikely to be a boy or girl, all five outcomes must be equally ieiy. Therefore, the probability of all four children being girls is 1/5. Explain the flaw in his reasoning. The argument is only correct if each child is equally likely to be a boy or girl. O The outcomes are not equally likely. O The sample space has less than 5 possible outcomes. O The sample space has more than 5 possible outcomes.
on a paper
HI! HELP ME WITH THIS PLEASE. THANK YOU VERY MUCH! The following hybrids are produced when white snowy owls are mated with brown barn owls: white barn owls, brown snowy owls, white snowy owls, and brown barn owls. The probabilities for each are 1/5, ¼, 9/20, and 1/10, respectively. If 9 owls are selected from this batch, find the probability that 2 are brown barn owls, 3 are white snowy owls, 1 is a brown snowy owl, and 3 are white barn owls.
Suppose you have just received a shipment of 30 modems. Although you don't know this, 8 of the modems are defective. To determine whether you will accept the shipment, you randomly select 9 modems and test them. If all 9 modems work, you accept the shipment. Otherwise, the shipment is rejected. What is the probability of accepting the shipment? The probability of accepting the shipment is...
41. In a dice game, one fair die is used. The players wins P20 if he rolls either a 1 or a 6. He loses P10 if he turns up any other face. What is the expected winning for one roll of the die? Answer must be: 0.0

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