2. You have a fair five-sided dic. The sides of the die are numbered from 1 to 5. Each die roll isindependent of all others, and all faces are equally likely to come out on top when the die is rolled.Suppose you roll the die twice.(a) Let event A to be "the total of two rolls is 10", event B be “at least one roll resulted in 5", andevent C be “at least onc roll resulted in 1.i. Is event A independent of event B?ii. Is event A independent, of event C?(b) Let event D be "the total of two rolls is 7", event E be “the difference between the two rolloutcomes is exactly 1", and event F be "the second roll resulted in a higher number than thefirst roll".i. Arc events E and F independent?ii. Are events E and F independent given event D?

Answered: 2. You have a fair five-sided dic. The…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose we roll two six-sided dice. Consider event A as getting an odd number on die 1, event B asgetting an even sum for the two dice. Are event A and B independent?
An experiment consists of rolling a fair die twice. Let A be the event that in the second roll the die lands 1, 2, or 5; B be the event that in the second roll the die lands 4, 5, or 6; and C be the event that the sum of the two outcomes from the two rolls is 9. Please choose the correct answer:
A pair of fair dice is rolled onoe, Suppose that you lose $7 if the dice sum to 5 and win $8 if the dice sum to 11 or 12. How much should you win or lose if any other number tums up in order for the game to be fair? To keep the game fair, you should (Do not round until the final answer. Then round to the nearest cent as needed.) if the dice sum to any other number
Each of the questions in this boxpertains to rollinga pair of fair dice. Find the probability that the sum is less than 5 and the sum is prime.
Question 2 Determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning. A computer is used to randomly select a number between 1 and 1000. Event A is selecting a number greater than 600. O 1; Simple event because it is an event that consists of a single outcome. O 400; Simple event because only one number is selected. O 600; Not a simple event because it is an event that consists of more than a single outcome. O 400; Not a simple event because it is an event that consists of more than a single outcome.
2.
Suppose you have an urn containing 3 red and 3 blue balls. You draw three balls at random. On each draw, if the ball is red you set it aside and if the ball is blue you put it back in the urn. What is the probability that the third draw is blue? (If you get a blue ball it counts as a draw even though you put it back in the urn.) O a. 1/125 O b. 267/500 O . 27/136 O d. 27/125 O e. 121/200
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
A six-sided die with faces labeled 1 to 6 will be rolled once. The six possible outcomes are listed. Note that each outcome has the same probability. Complete parts a through c. Write the probabilities as fractions.
3. Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0. i. If a fair 6-sided die is rolled once. If A is the event of "rolling an odd number," write out A and A° а. b. If A = {1,2,3,4} and B = {4,5,6}, write out A°, B°, AB, and AUB. i. When two fair die are thrown together: a. What is the probability that the dice total is 4?
Given P(A) = 0.10, P(B) = 0.63, P(C) = 0.53 and that events A, B, and C are independent, what is P(A, B, and C). Answer in decimal form. Round to 3 decimal places as needed.
Two unbalanced dice are thrown at the same time. The first die has the property that the probability of getting a side of 1 and 6 is three times the other side. While the second dice has the property that the probability of the appearance of the sides of the eye 3 and 4 is three times the probability of the other side. If X represents the appearance of the side of the first die and Y represents the appearance of the side of the second die. a. Find the joint probability mass function, P(x,y) b. Find the X and Y marginal probability mass functions c. Find E(X), E(Y), and E(XY)

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