Example 2.10.1 There are three dice in a bag. One has one red face, another has two red faces,and the third has three red faces. One of the dice is drawn at random from the bag, each die havingan equal chance of being drawn. The selected die is repeatedly rolled.(a) What is the probability that red shows on the first roll?(b) Given that red shows on the first roll, what is the conditional probability that red shows onthe second roll?(c) Given that red shows on the first three rolls, what is the conditional probability that the selecteddie has red on three faces?

Answered: Image /qna-images/answer/1b18327b-4679-4be0-85cf-bed62a65dd1c.jpg

Answered: Example 2.10.1 There are three dice in…

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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Is Lucas's first free throw shot independent of his second free throw shot? O The two free throws are dependent on each other. O The two free throws are independent of each other. O It is impossible to tell from the given information whether or not the two free throws independent of each other. What is the probability that Lucas makes both free throws?
Consider the following game: A player rolls two dice. If he rolls 7 or less then he loses the game. Otherwise, he selects at random as many cards from the full deck as the sum of the numbers that came up on the dice. The player wins if all four Aces are among the selected cards. (a) What is the winning probability for this game? (b) Someone tells that he played this game once and won. What is the probability that he rolled a sum of 10?
At a local restaurant, you are allowed to pick one side with your dinner. Because you can only choose one, your side choice is mutually exclusive of all the other sides to chose from. On any given day, there is a 0.34 chance you will pick an fries, and a 0.1 chance you will pick an veggies. Today, you do not pick an veggies; what is the probability you pick fries today?
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.
2 dice, one green and one black, are rolled once. Which of the following events are independent? 1. E= A 2 is rolled on the green die, F= A sum of 7 is rolled on both dice. 2. E= A 3 is rolled on the green die, F= A 5 is rolled on the black die. 3. E= A sum of 3 is rolled on both dice, F= A 4 is rolled on the black die. 4. E= A 2 is rolled on the green die, F= A sum of 8 is rolled on both dice.
3) Another bag of marbles contains 6 blue marbles and 1 green marble. Mary and Frank will draw a blue marble followed by a green marble, without replacing the first marble. Mary says the probability will be 649, and Frank says that the probability will be17 . Who is correct? Explain and justify your answer by showing work. _______________ is correct because ____________________________________________ ____________________________________________________________________________
Example 2.17 Of the voters in a city, 40% are Republicans and 60% are Democrats. Among the Republicans 70% are in favor of a bond issue, whereas 80% of the Democrats favor the issue. If a voter is selected at random in the city, what is the probability that he or she favor the bond issue?
Urn 1 contains 4 red and 6 white balls. Urn 2 contains 3 red and 6white balls. A ball is drawn from urn 1 and placed in urn 2. Then a ball is drawn from urn 2. If the ball drawn from urn 2 is red, what is the probability that the ball drawn from urn 1 was red?
Suppose I have a pair of standard, six-sided dice. For a single roll of the two dice, what is the probability that I roll doubles, which is when the results of the two dice are the same? Examples: 1 & 1, 2 & 2, ..., 6 & 6 You may assume that the dice and fair and that the two dice are independent.
4. Teddy lives life on the edge and gets dressed randomly every morning. This morning, he is randomly choosing a pair of shoes, a pair of pants, and a shirt from his closet which contains the following colors and corresponding quantities: Shoes: black (2) and brown (3) Pants: black (3) and brown (1) Shirt: white (2), brown (4) and black (6) What is the probability that Teddy randomly chooses shoes, pants and a shirt of the same color? A. 1/5 В. 2/5 С. 120 A B C D D. 3/20
An actuarial student studying for Exam P has an option to purchase probability books by Robert, Smith, and/or Taylor. A total of 72% of students buy only one of these books (with all books having the same probability), and 18% buy only two books (with each pair of books having the same probability). The probability that a student bought all three books given that he bought Robert's and Taylor's books is 40%. What is the probability that a student who did not buy Smith's book did not buy any book at all? A 10% B 11% 17% D 20% E 21%
2 dice, one green and one black, are rolled once. Which of the following events are independent?A. E = A 2 is rolled on the green die, F = A sum of 8 is rolled on both dice.B. E = A sum of 3 is rolled on both dice, F = A 4 is rolled on the black die.C. E = A 2 is rolled on the green die, F = A sum of 7 is rolled on both dice.D. E = A 3 is rolled on the green die, F = A 5 is rolled on the black die.

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