# 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?

Â© BrainMass Inc. brainmass.com December 24, 2021, 10:00 pm ad1c9bdddfhttps://brainmass.com/business/business-law/options-based-probability-making-profits-433221

## SOLUTION This solution is **FREE** courtesy of BrainMass!

The answers are in the attached Excel File.

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

i. Option 1:Â If you submit a price of $2M, you believe you will have a 50% probability of winning the contract.Â Â 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.Â If you win the contract and lose money, you get fired.Â Â

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

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 making a profit= 67% = 100% - 33.%

Three possibilities

1) Not winning the contract; Probability = 50.00%

2) Winning the contract and making a profit; Probability = 16.50% = 50.% x 33.%

3) Winning the contract and not making a profit; Probability = 33.50% = 50.% x 67.%

Total= 100.00%

Option 2

Probability of winning= 25%

Therefore, Probability of not winning= 75% = 100% - 25.%

Probability of making a profit at the price= 85%

Therefore, Probability of not making a profit= 15% = 100% - 85.%

Three possibilities

1) Not winning the contract; Probability = 75.00%

2) Winning the contract and making a profit; Probability = 21.25% = 25.% x 85.%

3) Winning the contract and not making a profit; Probability = 3.75% = 25.% x 15.%

Total= 100.00%

Option 1

Profit No Profit

Win 16.5% 33.5%

Not win 50%

Probability of not getting fired- (Not losing the contract and not losing money)= 16.5%

Option 2

Profit No Profit

Win 21.25% 3.75%

Not win 75%

Probability of not getting fired- (Not losing the contract and not losing money)= 21.25%

Since option 2 has better probability of not getting fired- select Option 2.

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

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

Option 1

Profit No Profit

Win 16.5% 33.5%

Not win 50%

Probability of winning a bonus of $75K (Winning the contract and making money)= 16.5%

Probability of winning a bonus of $50K (Winning the contract)= 33.5%

Expected Value of bonus

Probability Bonus

16.5% 75 $12.375 = 16.5% x 75

33.5% 50 $16.750 = 33.5% x 50

Total Expected Bonus= $29.125 K

Option 2

Profit No Profit

Win 21.25% 3.75%

Not win 75%

Probability of winning a bonus of $75K (Winning the contract and making money)= 21.25%

Probability of winning a bonus of $50K (Winning the contract)= 3.750%

Expected Value of bonus

Probability Bonus

21.25% 75 $15.9375 = 21.25% x 75

3.75% 50 $1.8750 = 3.75% x 50

Total Expected Bonus= $17.8125 K

Since option 1 has higher expected bonus - select Option 1.

Â© BrainMass Inc. brainmass.com December 24, 2021, 10:00 pm ad1c9bdddf>https://brainmass.com/business/business-law/options-based-probability-making-profits-433221