# Probability Question

a. You have prepared a proposal and are in the final stages of submitting your price. You have two options:

i. Option 1: If you submit a price of $2M, you believe you will have a 50% probability of winning the contract. However, you will only have a 33% probability of making a profit at that price.

ii. Option 2: If you submit a price of $2.5M, you believe you will have a 25% probability of winning the contract and an 85% chance of making a profit.

If you lose the contract, you get fired. If you win the contract and lose money, you get fired.

Which option should you chose to optimize your chances of keeping your job? Why?

b. You have gone to a new company and discover you are facing a similar decision. However, in this company, nobody ever gets fired. Instead, this company has a bonus system in place. If you win the contract you get a bonus of $50k. If you make money on the contract; you get a bonus of $25K.

Which option should you choose to maximize your bonus? Why?

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#### Solution Preview

The answers are in the attached Excel File.

a. You have prepared a proposal and are in the final stages of submitting your price. You have two options:

i. Option 1: If you submit a price of $2M, you believe you will have a 50% probability of winning the contract. However, you will only have a 33% probability of making a profit at that price.

ii. Option 2: If you submit a price of $2.5M, you believe you will have a 25% probability of winning the contract and an 85% chance of making a profit.

If you lose the contract, you get fired. If you win the contract and lose money, you get fired.

Which option should you chose to optimize your chances of keeping your job? Why?

Calculation of Probabilities

Option 1

Probability of winning= 50%

Therefore, Probability of not winning= 50% = 100% - 50.%

Probability of making a profit at the price= 33%

Therefore, Probability of not ...

#### Solution Summary

The solution compares two options based on probability of making profits.