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A game is played using a four-sided wooden top, with one of four letters on each face, A, B, C, or D. Players compete for a pot of tokens. A player spins the top and takes one of the following actions, depending on which letter faces up. If A faces up, the player neither adds nor subtracts tokens from the pot. • If B faces up, the player wins the entire pot of tokens. • If C faces up, the player wins half of the tokens in the pot, rounding up if the number is odd. •If D faces up, the player adds a token to the pot. Assume that each face of the top is equally likely to face upward and that the pot holds 25 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is (-1,0,13,25). Let the probability mass function be f(x)=P(X=x) and the cumulative probability function be F(x)=P(Xsx). Find f(24) and F(24). First, find the probability mass function f(x). (Type an ordered pair. Use a comma to separate answers as needed.) Now find f(24) f(24) = (Simplify your answer.) Find the cumulative probability function F(x)=P(Xsx). Choose the correct answer below. O A. O B. [0x<-1 -14x525 025

A game is played using a four-sided wooden top, with one of four letters on each face, A, B, C, or D. Players compete for a pot of tokens. A player spins the top and takes one of the following actions, depending on which letter faces up. If A faces up, the player neither adds nor subtracts tokens from the pot. • If B faces up, the player wins the entire pot of tokens. • If C faces up, the player wins half of the tokens in the pot, rounding up if the number is odd. •If D faces up, the player adds a token to the pot. Assume that each face of the top is equally likely to face upward and that the pot holds 25 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is (-1,0,13,25). Let the probability mass function be f(x)=P(X=x) and the cumulative probability function be F(x)=P(Xsx). Find f(24) and F(24). First, find the probability mass function f(x). (Type an ordered pair. Use a comma to separate answers as needed.) Now find f(24) f(24) = (Simplify your answer.) Find the cumulative probability function F(x)=P(Xsx). Choose the correct answer below. O A. O B. [0x<-1 -14x525 025

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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A game is played using a four-sided wooden top, with one of four letters on each face, A, B, C, or D. Players compete for a pot of tokens. A player spins the top and takes one of the following actions, depending on which letter faces up. • If A faces up, the player neither adds nor subtracts tokens from the pot. • If B faces up, the player wins the entire pot of tokens. • If C faces up, the player wins half of the tokens in the pot, rounding up if the number is odd. • If D faces up, the player adds a token to the pot. Assume that each face of the top is equally likely to face upward and that the pot holds 25 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {-1,0,13,25). Let the probability mass function be f(x)=P(X=x) and the cumulative probability function be F(x) = P(X ≤x). Find f(24) and F(24). First, find the probability mass function f(x). f(x) = {} (Type an ordered pair. Use a comma to separate answers as needed.) Now find f(24). f(24)= (Simplify your answer.) Find the cumulative probability function F(x) = P(X≤x). Choose the correct answer below. O A. O B. 0 x < -1 F(x)=11sx≤25 0 25<x Now find F(24). F(24)= (Simplify your answer.) 0.25 -1<x<0 F(x)= 0.5 0<x< 13 0.75 13<x<25 O O C. F(x)= x < -1 0.25 -1<x<0 0.75 0<x<25 25 sx O D. 0x<-1 0.25 -1<x<0 F(x)= 0.5 0<x<13 0.75 13<x<25 1 25sx
Transcribed Image Text:A game is played using a four-sided wooden top, with one of four letters on each face, A, B, C, or D. Players compete for a pot of tokens. A player spins the top and takes one of the following actions, depending on which letter faces up. • If A faces up, the player neither adds nor subtracts tokens from the pot. • If B faces up, the player wins the entire pot of tokens. • If C faces up, the player wins half of the tokens in the pot, rounding up if the number is odd. • If D faces up, the player adds a token to the pot. Assume that each face of the top is equally likely to face upward and that the pot holds 25 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {-1,0,13,25). Let the probability mass function be f(x)=P(X=x) and the cumulative probability function be F(x) = P(X ≤x). Find f(24) and F(24). First, find the probability mass function f(x). f(x) = {} (Type an ordered pair. Use a comma to separate answers as needed.) Now find f(24). f(24)= (Simplify your answer.) Find the cumulative probability function F(x) = P(X≤x). Choose the correct answer below. O A. O B. 0 x < -1 F(x)=11sx≤25 0 25<x Now find F(24). F(24)= (Simplify your answer.) 0.25 -1<x<0 F(x)= 0.5 0<x< 13 0.75 13<x<25 O O C. F(x)= x < -1 0.25 -1<x<0 0.75 0<x<25 25 sx O D. 0x<-1 0.25 -1<x<0 F(x)= 0.5 0<x<13 0.75 13<x<25 1 25sx
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