Question 1 You have a 4-sided die with sides numbered from 1 to 4. You perform thefollowing experiment:• You roll the 4-sided die and record the number.• If you recorded a 2, 3 or a 4, the experiment ends.• If you recorded a 1, you roll the die a second time, record the second number aswell, and the experiment ends.Assume that the die is fair, and that rolls are independent.Let N be the number of rolls, and X the sum of all recorded numbers.a) Define the sample space S of the experiment.b) Find the probability mass function (pmf) px(x) for X.c) Find P[N = 1|X = 3] and P[N = 2|X = 3].%3D Question 2 Alice has a coin that flips heads with probability p. She flips the coin n > 0times (assume the flips are independent).If exactly k of the n flips are heads, she wins $1. Otherwise she wins nothing.a) If 0 < k < n, what should p be to maximize Alice's expected winnings?b) If k = n, what should p be to maximize Alice's expected winnings? Explain whythis answer makes sense.

Since you have asked multiple question, according to our guidelines we will solve the first question…

Answered: Question 1 You have a 4-sided die with…

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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Similar questions

You roll an 8-sided die. Let A = {4, 5, 7, 8} and B {1, 3, 6, 7}. Find the following. S = { 1,2,3,4,5,6,7,8 A' = {{ 1,2,3,6 B' = { 2,4,5,8 P(A') = P(B') = n(A OR B') = %3D n(A' AND B) %3D P(A OR B') = P(A' AND B) = P(A| B') = P(A' | B) = %3D
30% of students take Physics 101 and 20% take Math146. Of the students who take Physics 101, 25% also take Math146. If a student is chosen at random find P( student takes Physics101 and Math146) O a. 0.3 O b. 0.2 O c. 0.25 O d. 0.83 One 0.075
a pair of dice is rolled once. Suppose that you lose 9$ if the dice sum to 5 and win 10$ if the dice sum to 11 or 8. How much should you win or lose if any other number turns up in order for the game to be fair?
You roll two fair dice. What is the P that the sum you roll is: D given 10?
An experiment consists of rolling a pair of fair dice, one red and one green. An outcome is an ordered pair (r,g), where r is the number on the red die and g is the number on the green die. List all outcomes of this experiment.
The fractions of colors in a population of squirrels is 0.73 red and 0.27 black. If two are chosen at random, what are the chances they have the same color? Give two digits past decimal.
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.
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