You roll a fair die.If you get a number greater than 4,you win $70.If not,you get to roll again.If you get a number greater than 4 the second time,you win $30.Otherwise you win nothing. Create a probability model for the amount you win at this game.

A) $268361636\begin{array} { l | c c c } \text { Amount won } & \$ 70 & \$ 30 & \$ 0 \\\hline \text { P(Amount won) } & \frac { 2 } { 6 } & \frac { 8 } { 36 } & \frac { 16 } { 36 }\end{array}$
B) $4368368361636\begin{array} { l | c c c c } \text { Amount won } & \$ 100 & \$ 70 & \$ 30 & \$ 0 \\\hline \mathrm { P } \text { (Amount won) } & \frac { 4 } { 36 } & \frac { 8 } { 36 } & \frac { 8 } { 36 } & \frac { 16 } { 36 }\end{array}$
C) $262626\begin{array} { l | c c c } \text { Amount won } & \$ 70 & \$ 30 & \$ 0 \\\hline \mathrm { P } \text { (Amount won) } & \frac { 2 } { 6 } & \frac { 2 } { 6 } & \frac { 2 } { 6 }\end{array}$
D) $4362362361636\begin{array} { l | c c c c } \text { Amount won } & \$ 100 & \$ 70 & \$ 30 & \$ 0 \\\hline \mathrm { P } \text { (Amount won) } & \frac { 4 } { 36 } & \frac { 2 } { 36 } & \frac { 2 } { 36 } & \frac { 16 } { 36 }\end{array}$
E) $2646\begin{array} { l | c c } \text { Amount won } & \$ 70 & \$ 30 \\\hline \text { P(Amount won) } & \frac { 2 } { 6 } & \frac { 4 } { 6 }\end{array}$

Question

You roll a fair die.If you get a number greater than 4,you win $70.If not,you get to roll again.If you get a number greater than 4 the second time,you win $30.Otherwise you win nothing. Create a probability model for the amount you win at this game.A)     Amount won  $ 70 $ 30 $ 0  P(Amount won)   2 6 8 36 16 36 \begin{array} { l | c c c } 	ext { Amount won }  &  \$ 70  &  \$ 30  &  \$ 0 \\hline 	ext { P(Amount won)  }  &  \frac { 2 } { 6 }  &  \frac { 8 } { 36 }  &  \frac { 16 } { 36 }\end{array}  Amount won   P(Amount won)   ​ $70 6 2 ​ ​ $30 36 8 ​ ​ $0 36 16 ​ ​ ​ B)     Amount won  $ 100 $ 70 $ 30 $ 0 P  (Amount won)   4 36 8 36 8 36 16 36 \begin{array} { l | c c c c } 	ext { Amount won }  &  \$ 100  &  \$ 70  &  \$ 30  &  \$ 0 \\hline \mathrm { P } 	ext { (Amount won)  }  &  \frac { 4 } { 36 }  &  \frac { 8 } { 36 }  &  \frac { 8 } { 36 }  &  \frac { 16 } { 36 }\end{array}  Amount won  P  (Amount won)   ​ $100 36 4 ​ ​ $70 36 8 ​ ​ $30 36 8 ​ ​ $0 36 16 ​ ​ ​ C)     Amount won  $ 70 $ 30 $ 0 P  (Amount won)   2 6 2 6 2 6 \begin{array} { l | c c c } 	ext { Amount won }  &  \$ 70  &  \$ 30  &  \$ 0 \\hline \mathrm { P } 	ext { (Amount won)  }  &  \frac { 2 } { 6 }  &  \frac { 2 } { 6 }  &  \frac { 2 } { 6 }\end{array}  Amount won  P  (Amount won)   ​ $70 6 2 ​ ​ $30 6 2 ​ ​ $0 6 2 ​ ​ ​ D)     Amount won  $ 100 $ 70 $ 30 $ 0 P  (Amount won)   4 36 2 36 2 36 16 36 \begin{array} { l | c c c c } 	ext { Amount won }  &  \$ 100  &  \$ 70  &  \$ 30  &  \$ 0 \\hline \mathrm { P } 	ext { (Amount won)  }  &  \frac { 4 } { 36 }  &  \frac { 2 } { 36 }  &  \frac { 2 } { 36 }  &  \frac { 16 } { 36 }\end{array}  Amount won  P  (Amount won)   ​ $100 36 4 ​ ​ $70 36 2 ​ ​ $30 36 2 ​ ​ $0 36 16 ​ ​ ​ E)     Amount won  $ 70 $ 30  P(Amount won)   2 6 4 6 \begin{array} { l | c c } 	ext { Amount won }  &  \$ 70  &  \$ 30 \\hline 	ext { P(Amount won)  }  &  \frac { 2 } { 6 }  &  \frac { 4 } { 6 }\end{array}  Amount won   P(Amount won)   ​ $70 6 2 ​ ​ $30 6 4 ​ ​ ​

Angela Reji Philip · Accepted Answer

Final Answer : A, Explanation :   The probability of winning $70 is   2 6 \frac{2}{6} 6 2 ​   because there are 2 outcomes (5 or 6) out of 6 that result in winning $70 on the first roll. The probability of winning $30 is   4 6 × 2 6 = 8 36 \frac{4}{6} 	imes \frac{2}{6} = \frac{8}{36} 6 4 ​ × 6 2 ​ = 36 8 ​   because you must first not win on the first roll (4 outcomes out of 6) and then win on the second roll (2 outcomes out of 6). The probability of winning $0 is   4 6 × 4 6 = 16 36 \frac{4}{6} 	imes \frac{4}{6} = \frac{16}{36} 6 4 ​ × 6 4 ​ = 36 16 ​   because you must not win on both rolls, each having 4 outcomes out of 6 that don't result in a win.

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