Exercise 2. In this question it is fine to use a calculator or computer to express your answers asdecimals, rather than as fractions.In class we played a game in which two players, whom we shall call A and B, form two randomvariables X₁ and X₂ by each rolling two dice.X₁ (A's r.v.) is the sum of the two numbers shown on the dice. X₂ (B's r.v.) is 1.5 times thelarge of the two numbers shown.(a) Calculate the probability that A beats B in a round of the game.(b) Calculate the probability that A and B get equal scores.(c) Given that one player wins, calculate the conditional probability that the winning player isA.

Given that A and B form two random variables X1 and X2 by each rolling two dice. X1 is the sum of…

Answered: Exercise 2. In this question it is fine…

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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. Suppose an exam consists of multiple-choice questions, with each question having 5 options. Exactlyone of the five options is the correct answer. Suppose 24 points are awarded for a correctly answeredquestion.(a) How many points should be deducted for an incorrectly answered question, so that for a studentguessing randomly, the expected score on a question is zero?(b) If a student is able to correctly eliminate one option as a possible correct answer but is still guessingrandomly, what happens to his/her expected score for that question? Use your answer to (a) asthe number of points being deducted for an incorrect answer.
Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 5. You are playing Scrabble and you draw seven tiles: M, A, T, C, H, E, S. You line them up in some random order on your tile rack (assume all orderings are equally likely). The events M, T, and S are defined as follows: M: The tiles M, A, T, H appear consecutively. T: The tile T appears exactly in the middle (fourth position). S: The tile S is either in the first position or in the final position. Calculate the probability of each event; that is, p(M), p(T), and p(S). 5.1 5.2 What is p(MIT)? 5.3 What is p(MIS)? 5.4 5.5 What is p(T|S)? Consider all pairs of events: (M,T), (M,S), and (T,S). Which pairs of events are independent and which pairs of events are not independent? Justify your answer.
Kaolin is taking a multiple choice math test. Each question has seven presented answers, but only one is correct. If Kaolin guesses randomly for each of the nineteen questions the test has, determine the probability that Kaolin gets at most one question correct. A. 618719 B. 25719 C. (190) +(191)719 D 61825719 E. (61)(191)719
1. Use this table for the following questions: Female Male TotalShort Hair 20 40 60 Long Hair 30 10 40 Total 50 50 100 a. Complete a total probability table.b. Complete a row probability tablec. Complete a column probability table.d. The probability that a student does not have long hair. _________e. The probability that a student is male or has short hair. ________f. The probability that a student is a female and has long hair. _________g. The probability that a student is male, given that the student has long hair. _________h. The probability that a student has long hair, given that the student is male. _________i. Of all the female students, the probability that a student has short hair. ________j. Of all students with long hair, the probability that a student is female. _________k. The probability that a student is female or has long hair.…
For Parts A, B, and C, use the experiment below. Show all work. Two fair six-sided dice are rolled. Part A: How many outcomes are in the sample space of the experiment? Part B: What is the probability the sum of the two dice will be greater than or equal to 10? Part C: Laura and Bethany want to decide who fills the car with gasoline for their upcoming trip. Laura will fill the car if the sum of the dice is greater than or equal to 10, and Bethany will fill the car if the sum of the dice is less than 5 If the sum of the dice is any other value, the result is discarded. Does this method provide a fair way to decide who fills the car with gasoline? Provide a supporting explanation.
Consider a game of rolling a single die, with the outcome as the random variable X. A player gains $10 if the outcome is {1, 2, 3} and a player loses $5 if the outcome is (4, 5, or 6}. It does not cost anything to play the game. Calculate o. Round to 2 decimal places.
A board game uses the deck of 20 cards shown to the right. If one card is drawn, determine the probability that the card shows a lion or a 3. Y R. Y 3 4 17 2 3 4 5 *2 3* 4 5 % 1 2 3 4 s ..... The probability of selecting a lion or a 3 is. (Type an integer or a simplified fraction.) Next 2.
A. Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35% of the time, four events 25% of the time, three events 20% of the time, two events 10% of the time, one event 5% of the time, and no event 5% of the time. What values does x take on? (Enter your answers as a comma-separated list.) B. Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 25% of the time, four events 25% of the time, three events 20% of the time, two events 15% of the time, one event 10% of the time, and no events 5% of the time. Find the probability that Javier volunteers for less than three events each month. (Enter an exact number as an integer, fraction, or decimal.) P(x < 3) =
Questions A, B, and C. Please!

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