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There are three contestants in a game. The game is played as follows: 3 tokens that are mumbered 1, 2, and 3 are placed in a box. Each contestant selects a token with replacement (i.e, contestants select a token, announces the mumber and places the token back to the box). The person(s) who picked the largest number share a cash prize of $300 equally among them. (a) Define the sample space representing the game. (b) What is the probability that winners receive $100 cach. (c) What is the probability that there is a single winner who takes the $300? (d) How do your answers to parts (b) and (c) change when tokens are selected without replacement?

There are three contestants in a game. The game is played as follows: 3 tokens that are mumbered 1, 2, and 3 are placed in a box. Each contestant selects a token with replacement (i.e, contestants select a token, announces the mumber and places the token back to the box). The person(s) who picked the largest number share a cash prize of $300 equally among them. (a) Define the sample space representing the game. (b) What is the probability that winners receive $100 cach. (c) What is the probability that there is a single winner who takes the $300? (d) How do your answers to parts (b) and (c) change when tokens are selected without replacement?

A First Course in Probability (10th Edition)
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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There are three contestants in a game. The game is played as follows: 3 tokens that are numbered 1, 2, and 3 are placed in a box. Each contestant selects a token with replacement (i.e, contestants select a token, announces the mumber and places the token back to the box). The person(s) who picked the largest number share a cash prize of $300 equally among them. (a) Define the sample space representing the game. (b) What is the probability that winners receive $100 each. (c) What is the probability that there is a single winner who takes the $3002 (d) How do your answers to parts (b) and (c) change when tokens are selected without replacement?
Transcribed Image Text:There are three contestants in a game. The game is played as follows: 3 tokens that are numbered 1, 2, and 3 are placed in a box. Each contestant selects a token with replacement (i.e, contestants select a token, announces the mumber and places the token back to the box). The person(s) who picked the largest number share a cash prize of $300 equally among them. (a) Define the sample space representing the game. (b) What is the probability that winners receive $100 each. (c) What is the probability that there is a single winner who takes the $3002 (d) How do your answers to parts (b) and (c) change when tokens are selected without replacement?
Axioms of Probability Also Note: 1. P(S)=1 For any two events A and B, 2. For any event E, 0< P(E) < 1 P(A) = P(AN B) + P(AN B') 3. For any two mutually exclusive events, and P(EUF) = P(E)+ P(F) P(AN B) P(A|B)P(B). Events A and B are independent if: Addition Rule P(EUF) = P(E)+ P(F) – P(ENF) Р(AВ) — Р(А) or Conditional Probability Р(An B) %3D P(A)Р(В). Р(BJA) — P(ANB) P(A) Bayes' Theorem: Total Probability Rule Р(АВ)P(B) Р(А|B)Р(В) + Р(A|B')P(В') P(A)-P(A | Β) P(Β) + P(A| Β') P(Β') P(B|A) Similarly, Similarly, Р(A) —DР(A|E,)Р(E) + P(A|E2) Р(E)+ P(B|E1)P(E1) P(B|E1)P(E1)+P(B|E2)P(E2) + · · · + P(B|Er)P(Ex) ...+ P(A|Ek)P(Ek) P(E1\B)
Transcribed Image Text:Axioms of Probability Also Note: 1. P(S)=1 For any two events A and B, 2. For any event E, 0< P(E) < 1 P(A) = P(AN B) + P(AN B') 3. For any two mutually exclusive events, and P(EUF) = P(E)+ P(F) P(AN B) P(A|B)P(B). Events A and B are independent if: Addition Rule P(EUF) = P(E)+ P(F) – P(ENF) Р(AВ) — Р(А) or Conditional Probability Р(An B) %3D P(A)Р(В). Р(BJA) — P(ANB) P(A) Bayes' Theorem: Total Probability Rule Р(АВ)P(B) Р(А|B)Р(В) + Р(A|B')P(В') P(A)-P(A | Β) P(Β) + P(A| Β') P(Β') P(B|A) Similarly, Similarly, Р(A) —DР(A|E,)Р(E) + P(A|E2) Р(E)+ P(B|E1)P(E1) P(B|E1)P(E1)+P(B|E2)P(E2) + · · · + P(B|Er)P(Ex) ...+ P(A|Ek)P(Ek) P(E1\B)
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