A company bids on two contracts.It anticipates a profit of $50,000 if it gets the larger contract and a profit of $20,000 if it gets the smaller contract.It estimates that there's a 20% chance of winning the larger contract and a 60% chance of winning the smaller contract. Create a probability model for the company's profit.Assume that the contracts will be awarded independently.A) Profit $ 0 $ 20 , 000 $ 50 , 000 $ 70 , 000 P(Profit) 0.32 0.48 0.08 0.12 \begin{array} { l | l c c c } ext { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 & \$ 70,000 \\hline ext { P(Profit) } & 0.32 & 0.48 & 0.08 & 0.12\end{array} Profit P(Profit) $0 0.32 $20 , 000 0.48 $50 , 000 0.08 $70 , 000 0.12 B) Profit $ 0 $ 20 , 000 $ 50 , 000 $ 70 , 000 P(Profit) 0.08 0.6 0.2 0.12 \begin{array} { l | l c c c } ext { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 & \$ 70,000 \\hline ext { P(Profit) } & 0.08 & 0.6 & 0.2 & 0.12\end{array} Profit P(Profit) $0 0.08 $20 , 000 0.6 $50 , 000 0.2 $70 , 000 0.12 C) Profit $ 0 $ 20 , 000 $ 50 , 000 P(Profit) 0.2 0.6 0.2 \begin{array} { l | c c c } ext { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 \\hline ext { P(Profit) } & 0.2 & 0.6 & 0.2\end{array} Profit P(Profit) $0 0.2 $20 , 000 0.6 $50 , 000 0.2 D) Profit $ 0 $ 20 , 000 $ 50 , 000 $ 70 , 000 P(Profit) 0.32 0.48 0.08 0.8 \begin{array} { l | l c c c } ext { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 & \$ 70,000 \\hline ext { P(Profit) } & 0.32 & 0.48 & 0.08 & 0.8\end{array} Profit P(Profit) $0 0.32 $20 , 000 0.48 $50 , 000 0.08 $70 , 000 0.8 E) Profit $ 0 $ 20 , 000 $ 50 , 000 P(Profit) 0.32 0.48 0.08 \begin{array} { l | c c c } ext { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 \\hline ext { P(Profit) } & 0.32 & 0.48 & 0.08\end{array} Profit P(Profit) $0 0.32 $20 , 000 0.48 $50 , 000 0.08

Question

A company bids on two contracts.It anticipates a profit of $50,000 if it gets the larger contract and a profit of $20,000 if it gets the smaller contract.It estimates that there's a 20% chance of winning the larger contract and a 60% chance of winning the smaller contract. Create a probability model for the company's profit.Assume that the contracts will be awarded independently.A)     Profit  $ 0 $ 20 , 000 $ 50 , 000 $ 70 , 000  P(Profit)   0.32 0.48 0.08 0.12 \begin{array} { l | l c c c } 	ext { Profit }  &  \$ 0  &  \$ 20,000  &  \$ 50,000  &  \$ 70,000 \\hline 	ext { P(Profit)  }  &  0.32  &  0.48  &  0.08  &  0.12\end{array}  Profit   P(Profit)   ​ $0 0.32 ​ $20 , 000 0.48 ​ $50 , 000 0.08 ​ $70 , 000 0.12 ​ ​ B)     Profit  $ 0 $ 20 , 000 $ 50 , 000 $ 70 , 000  P(Profit)   0.08 0.6 0.2 0.12 \begin{array} { l | l c c c } 	ext { Profit }  &  \$ 0  &  \$ 20,000  &  \$ 50,000  &  \$ 70,000 \\hline 	ext { P(Profit)  }  &  0.08  &  0.6  &  0.2  &  0.12\end{array}  Profit   P(Profit)   ​ $0 0.08 ​ $20 , 000 0.6 ​ $50 , 000 0.2 ​ $70 , 000 0.12 ​ ​ C)     Profit  $ 0 $ 20 , 000 $ 50 , 000  P(Profit)   0.2 0.6 0.2 \begin{array} { l | c c c } 	ext { Profit }  &  \$ 0  &  \$ 20,000  &  \$ 50,000 \\hline 	ext { P(Profit)  }  &  0.2  &  0.6  &  0.2\end{array}  Profit   P(Profit)   ​ $0 0.2 ​ $20 , 000 0.6 ​ $50 , 000 0.2 ​ ​ D)     Profit  $ 0 $ 20 , 000 $ 50 , 000 $ 70 , 000  P(Profit)   0.32 0.48 0.08 0.8 \begin{array} { l | l c c c } 	ext { Profit }  &  \$ 0  &  \$ 20,000  &  \$ 50,000  &  \$ 70,000 \\hline 	ext { P(Profit)  }  &  0.32  &  0.48  &  0.08  &  0.8\end{array}  Profit   P(Profit)   ​ $0 0.32 ​ $20 , 000 0.48 ​ $50 , 000 0.08 ​ $70 , 000 0.8 ​ ​ E)     Profit  $ 0 $ 20 , 000 $ 50 , 000  P(Profit)   0.32 0.48 0.08 \begin{array} { l | c c c } 	ext { Profit }  &  \$ 0  &  \$ 20,000  &  \$ 50,000 \\hline 	ext { P(Profit)  }  &  0.32  &  0.48  &  0.08\end{array}  Profit   P(Profit)   ​ $0 0.32 ​ $20 , 000 0.48 ​ $50 , 000 0.08 ​ ​

Sujoy Samanta · Accepted Answer

Final Answer : A, Explanation :  The probabilities are calculated as follows: - P($0) = P(not winning the larger contract) * P(not winning the smaller contract) = 0.8 * 0.4 = 0.32.- P($20,000) = P(not winning the larger contract) * P(winning the smaller contract) = 0.8 * 0.6 = 0.48.- P($50,000) = P(winning the larger contract) * P(not winning the smaller contract) = 0.2 * 0.4 = 0.08.- P($70,000) = P(winning the larger contract) * P(winning the smaller contract) = 0.2 * 0.6 = 0.12.

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