Problem 1. MIT students sometimes delay laundry for a few days. Assume all randomvalues described below are mutually independent.(a) A busy student must complete 3 problem sets before doing laundry. Each problemset requires 1 day with probability 2/3 and 2 days with probability 1/3. Let B be thenumber of days a busy student delays laundry. What is E [B]?Example: If the first problem set requires 1 day and the second and third problem setseach require 2 days, then the student delays for B = 5 days.

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Answered: Problem 1. MIT students sometimes delay…

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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3. A retailer sells two brands of batteries that experience indicates are equal in demand. If he stocks two of each brand (which means he has 4 batteries in his store), what is the probability that a customer seeking to purchase two batteries, purchases the same brand? 1/3 2/3 01/2 1/4
Solve it correctly and clear
Suppose that each time Bar-bie throws a dart, she has a 3/4 probability of getting a bullseye. If Barbie shoots three darts, what is the probability that she gets a bullseye on at least two of them?
3. An unloaded, 4-sided dice is rolled twice. Let X be the maximum number obtained from the two rolls, and Y be the minimum number from the two rolls. (The dice can show the numbers 1, 2, 3, or 4, each with probability 1/4. As an example, if the two rolls are 1 followed by 3, then X = 3 and Y = 1.) (a) Find the joint pmf of X and Y. (b) Find the conditional pmf of X given that Y = 2. (Hint: part (a) is similar to a problem from Modelling Uncertainty. Please express your answers in table form, and please use fractions in lowest terms.)
ag I contains 2 White chips and 1 red chip and Bag II contains 2 red chips and one white chip. A chip is selected at random from g I and transferred to Bag II. Then a chip is selected at random from Bag II. If the selected chip is red, what is the probability that e transferred chip was white? 317 B 2/3 O 1/3 4/7
Example 7: If 3 balls are distributed to 4 cells, numbered as 1, 2, 3, 4. Find the probability that each cell numbered 1, 2, 3 will contain exactly one ball.
n = {1, 2, 3, 4} with each point carrying probability 1/4. Let A1 = {1, 2}, A2 = {1, 3}, A3 = {1, 4}. Then any two of A1, A2, A3 are independent, but A 1 , A 2, A 3 are not independen
1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
1.Mayank plays exactly one sport everyday. It can be football or basketball or chess. Forhim, the probability of playing chess on a random day is twice as that of playing footballand one third of the probability of playing basketball. What is the probability that in thenext week, he will play basketball in 3 days, chess in 2 days and football in the remainingdays?
Please help me fix problem D,E,F, Thank you!

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