1) Player A, B, and C play a quiz game. For each question, a player who rings a buzzer first has an opportunity to answer the question. For each question, only one player can answer the question, and player A, B, and C have 20%, 30%, and 50% chance of ringing the buzzer respectively. Once given an opportunity to answer, player A, B, and C have 50%, 40%, and 30% chance of making the right guess respectively. Questions are independent to each other, and every question is answered. (d) Suppose that the players play the quiz game until player A gives the correct answer. Denote the total number of games played by N including the last question answered correctly by A, and the number of correct answers by X including the last answer from A. Find the conditional pmf of X given N = n, i.e., find the probability mass function of X|N = n. (e) Suppose the setting and the notations are the same as in (d). Find the expectation of the number of the correct answers, i.e., find E[X].
1) Player A, B, and C play a quiz game. For each question, a player who rings a buzzer first has an opportunity to answer the question. For each question, only one player can answer the question, and player A, B, and C have 20%, 30%, and 50% chance of ringing the buzzer respectively. Once given an opportunity to answer, player A, B, and C have 50%, 40%, and 30% chance of making the right guess respectively. Questions are independent to each other, and every question is answered. (d) Suppose that the players play the quiz game until player A gives the correct answer. Denote the total number of games played by N including the last question answered correctly by A, and the number of correct answers by X including the last answer from A. Find the conditional pmf of X given N = n, i.e., find the probability mass function of X|N = n. (e) Suppose the setting and the notations are the same as in (d). Find the expectation of the number of the correct answers, i.e., find E[X].
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter0: Preparing For Algebra
Section: Chapter Questions
Problem 62PRT
Related questions
Question
Transcribed Image Text:1) Player A, B, and C play a quiz game. For each question, a player who rings a buzzer first
has an opportunity to answer the question. For each question, only one player can answer
the question, and player A, B, and C have 20%, 30%, and 50% chance of ringing the buzzer
respectively. Once given an opportunity to answer, player A, B, and C have 50%, 40%,
and 30% chance of making the right guess respectively. Questions are independent to each
other, and every question is answered.
![(d) Suppose that the players play the quiz game until player A gives the correct answer.
Denote the total number of games played by N including the last question answered
correctly by A, and the number of correct answers by X including the last answer
from A. Find the conditional pmf of X given N = n, i.e., find the probability mass
function of X|N = n.
(e) Suppose the setting and the notations are the same as in (d). Find the expectation
of the number of the correct answers, i.e., find E[X].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F008f8cce-1e45-43a4-8b17-46721d7357f5%2F795a7d60-ad75-46c6-84c9-9bb1cd4db709%2Ffo8g3w_processed.png&w=3840&q=75)
Transcribed Image Text:(d) Suppose that the players play the quiz game until player A gives the correct answer.
Denote the total number of games played by N including the last question answered
correctly by A, and the number of correct answers by X including the last answer
from A. Find the conditional pmf of X given N = n, i.e., find the probability mass
function of X|N = n.
(e) Suppose the setting and the notations are the same as in (d). Find the expectation
of the number of the correct answers, i.e., find E[X].
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