Asked by Brookelynne Verrette on Jul 22, 2024
Verified
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) 0.320.480.080.12\begin{array} { l | l c c c } \text { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 & \$ 70,000 \\\hline \text { P(Profit) } & 0.32 & 0.48 & 0.08 & 0.12\end{array} Profit P(Profit) $00.32$20,0000.48$50,0000.08$70,0000.12
B) Profit $0$20,000$50,000$70,000 P(Profit) 0.080.60.20.12\begin{array} { l | l c c c } \text { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 & \$ 70,000 \\\hline \text { P(Profit) } & 0.08 & 0.6 & 0.2 & 0.12\end{array} Profit P(Profit) $00.08$20,0000.6$50,0000.2$70,0000.12
C) Profit $0$20,000$50,000 P(Profit) 0.20.60.2\begin{array} { l | c c c } \text { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 \\\hline \text { P(Profit) } & 0.2 & 0.6 & 0.2\end{array} Profit P(Profit) $00.2$20,0000.6$50,0000.2
D) Profit $0$20,000$50,000$70,000 P(Profit) 0.320.480.080.8\begin{array} { l | l c c c } \text { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 & \$ 70,000 \\\hline \text { P(Profit) } & 0.32 & 0.48 & 0.08 & 0.8\end{array} Profit P(Profit) $00.32$20,0000.48$50,0000.08$70,0000.8
E) Profit $0$20,000$50,000 P(Profit) 0.320.480.08\begin{array} { l | c c c } \text { Profit } & \$ 0 & \$ 20,000 & \$ 50,000 \\\hline \text { P(Profit) } & 0.32 & 0.48 & 0.08\end{array} Profit P(Profit) $00.32$20,0000.48$50,0000.08
Probability Model
A mathematical representation of a random process, outlining the possible outcomes and their associated probabilities.
Larger Contract
A contract that is significant in terms of value, scope, or importance, often involving considerable resources or high stakes.
Smaller Contract
A contractual agreement of less scope or value compared to others, often involving fewer obligations or complexities.
- Learn to create probability models for various scenarios.
- Understand the concepts of independence and dependent events in probability.
Verified Answer
SS
Sujoy SamantaJul 25, 2024
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.
Learning Objectives
- Learn to create probability models for various scenarios.
- Understand the concepts of independence and dependent events in probability.