Exercise 4. (a) Two people play a dice game. Each throws a regular 6 sided die. The perso with the largest number wins. (i) What is the probability that they throw exactly the same number (so no-one wins)? (ii) Calculate the probability that player 1 wins in two ways, (1.) using conditional probabilit conditioned on all the possible numbers that player 1 could throw, (2.) by arguing that, given th one player wins, then it must be player 1 or player 2 with equal probability. Check that your tw solution methods yield identical answers.

Exercise 4. (a) Two people play a dice game. Each throws a regular 6 sided die. The perso with the largest number wins. (i) What is the probability that they throw exactly the same number (so no-one wins)? (ii) Calculate the probability that player 1 wins in two ways, (1.) using conditional probabilit conditioned on all the possible numbers that player 1 could throw, (2.) by arguing that, given th one player wins, then it must be player 1 or player 2 with equal probability. Check that your tw solution methods yield identical answers.

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...

See similar textbooks

Similar questions

Teams A and B are in a seven-game playoff series; the team that wins four games is the team that wins the series. Assume that both teams are evenly matched (i.e., the probability of winning each game is 50/50). (a) Team A won the first two games. What is the probability that team B will win the series? (b) Continue to assume that Team A has already won two games, but the teams are not evenly matched. Assume that B is a better team. It’s better in that its probability of beating Team A in any one game is .60. What is the probability that Team B will win the series? Pls solve via binomial theorem
The students in a class are selected at random, one after another, for an examination. Find the probability P that the boys and girls in the class arranged alternately if sds-allidsong ad (i) The class consists of 4 boys and 3 girls (ii) The class consists of 3 boys and 3 girls
A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 0.9, $50 0.1. Over many weeks, what is a worker's expected weekly bonus? a) (10+50) / 2 = $30 b) 10x0.9 + 50*0.1 = $14 c) (10*0.9 + 50*0.1) / 2 = $7 d) (10 + 50) / 10 = $6
The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively. Find the probability that in this 30-minute period (a) more than 2 cars receive gas; (b) at most 4 cars receive gas; (C) 4 or more cars receive gas
The probability that a person who identifies as male will be color-blind is 0.036. Find the probabilities that in a group of 54 people who identify as male, the following will be true. (a) Exactly 5 are color-blind. (b) No more than 5 are color-blind. (c) At least 1 is color-blind.
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (1) the youngest is a girl, (ii) at least one is a girl?
Of three events, A, B, and C, suppose events A and B are independent and events B and C are mutually exclusive. Their probabilities are P(A) = .7 , P(C) =.3 and P(B) =.2 Calculate the probabilities that (a) Both B and C occur. (c) B does not occur. (d) All three events occur. (b) At least one of A and B occurs.
Suppose the probability of a customer placing an order at a pizza place for a pepperoni pizza is 0.6, and for something else with probability 0.4. We assume if a customer calls the pizza place, he orders something, and that all incoming calls are indepen- dent. What is the probability that the pizza place will get the first pepperoni pizza order on the 4th call of the day?
Events A and B are mutually exclusive. Suppose event A Occurs with probability 0.58 and event B occurs with probability 0.32. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that B occurs but A does not occur. (b) Compute the probability that neither the event A nor the event B occurs.
If you have 4 red cards and 20 blue cards in your right hand, but your left hand is empty. Your friend has selected 4 cards without replacement in random and put them in your left hand. Then, he selected a card in random from your left hand. The conditional probability that two red cards and two blue cards were moved from your right hand to your left hand given that the card selected from your left hand is blue is: Select one: a. 0.3671 b. 0.4632 c. 0.0644 d. 0.4895 e. 0.3974
I need the answer as soon as possible