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Hi,
I’ve problem getting the correct answer for these 2 questions. Appreciate your guidance.
Q1. A Company has constructed a model for predicting profits. Net profit or loss depends on 2 variables: gross profit and overheads. The following are independent probability distributions of the 2 variables.
Gross profit Probability Overheads Probability
12,000.00 0.1 6,000.00 0.3
6,000.00 0.4 4,000.00 0.3
4,000.00 0.4 3,000.00 0.3
3,000.00 0.1 2,000.00 0.1What is the probability that the company will make a positive net profit?
Answer: 0.55
Q2. The directors of GHY plc are considering a new project that is subject to
considerable uncertainty.The following costs and revenues have been estimated for the first year:
Cost Probability Revenue Probability
100,000 0.1 120,000 0.2
150,000 0.2 150,000 0.3
200,000 0.4 180,000 0.4
250,000 0.3 200,000 0.1Assuming that the costs and revenues are independent of each other, what is the probability of a loss occuring?
Answer: 0.70
Q1: For a profit gross profit has to be more than overheads. So:
If GP is 12, there will be a profit. Prob of GP = 12 to occur is 0.1
If GP is 6, there will be a profit if OH = 4, 3 or 2. Prob = 0.4 x (0.3 + 0.3 + 0.1) = 0.28
If GP is 4, there will be a profit if OH = 3, or 2. The probability of these events occurring together is 0.4 x (0.3 + 01.) = 0.16
If GP = 3, there will be a profit if OH = 2. Probability = 0.1 x 0.1 = 0.01Sum of probabilities = 0.1 + 0.28 + 0.16 + 0.01 = 0.55
Q2: For a loss costs must be > revenue
If costs are 100, there is no chance of a loss.
If costs are 150, a loss occurs only if revenue is 120. Prob = 0.2 x 0.2 = 0.04
If costs are 200, a loss occurs if revenue = 120, 150 or 180. Prob = 0.4 x (0.2 + 0.3 + 0.4) = 0.36
If costs are 250, a loss will occur. Prob = 0.3Sum of probabilities = 0.04 + 0.36 + 0.3 = 0.7
HTH
Thank you so much. It’s a great help for a self study student like me. Really appreciate your time and effort.
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