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 Find f(28) and F(28). First, find the probability mass function f(x) (Type an ordered pair. Use a comma to separate answers as needed.) Now find f(28). f(28)= (Simplify your answer.) Find the cumulative probability function F(x)=P(Xsx). Choose the correct answer below. OA. O B. FOX 10 x<-1 0.25-16x40 0.75 0x<20 Now find F(28). F(28)= (Simplify your answer.) tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is (-1.0.15.29). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x)=P(X≤x). 0.25 -15x40 F00=0.5 0x<15 0.75 15x20 O C. 0x<-1 0.25-15x40 F05 0x<15 0.75 15x20 296x O D. (0xx-1)
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 Find f(28) and F(28). First, find the probability mass function f(x) (Type an ordered pair. Use a comma to separate answers as needed.) Now find f(28). f(28)= (Simplify your answer.) Find the cumulative probability function F(x)=P(Xsx). Choose the correct answer below. OA. O B. FOX 10 x<-1 0.25-16x40 0.75 0x<20 Now find F(28). F(28)= (Simplify your answer.) tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is (-1.0.15.29). Let the probability mass function be f(x) = P(X=x) and the cumulative probability function be F(x)=P(X≤x). 0.25 -15x40 F00=0.5 0x<15 0.75 15x20 O C. 0x<-1 0.25-15x40 F05 0x<15 0.75 15x20 296x O D. (0xx-1)
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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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 29 tokens. Let the random variable X be the amount of tokens won by a player. Thus, the range of X is {-1,0,15,29}. Let the probability mass function be f(x)=P(X=x) and the cumulative probability function be F(x) = P(X ≤x).
Find f(28) and F(28).
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(28).
f(28)= (Simplify your answer.)
Find the cumulative probability function F(x)=P(X≤x). Choose the correct answer below.
O A.
O B.
F(x)=
0 x < -1
0.25 -1<x<0
0.75 0<x<29
29 sx
Now find F(28).
F(28)= (Simplify your answer.)
0.25 -1<x<0
F(x)= 0.5 0≤x<15
0.75 15<x<29
C
O C.
0
x < -1
0.25 -1<x<0
F(x) = 0.5 0≤x<15
0.75 15<x<29
29 sx
O D.
0x< -1
F(x)=1-1sxs 29
0 29<x
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