OfficeQuip is a small office supply firm that is currently bidding on furniture and office equipment contracts?
jon l asked:
OfficeQuip is a small office supply firm that is currently bidding on furnature and office equipment contracts with four different potential customers who are of comparable size. For each contract, OfficeQuip would gain a profit of $50,000 if that contract were accepted, so the compant could make as little as $0 or as much as $200,000. The four potential customers are making independent decisions, and in each case the probability that OfficeQuip will receive the contract is 0.40. When all the decisions have been made, what is the probability that OfficeQuip will receive none of the contracts? Exactly one of the contracts? Exactly two of the contracts? Exactly three of the contracts? All four contracts? Overall, what is OfficeQuip’s expected profit in this business procurement venture?
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OfficeQuip is a small office supply firm that is currently bidding on furnature and office equipment contracts with four different potential customers who are of comparable size. For each contract, OfficeQuip would gain a profit of $50,000 if that contract were accepted, so the compant could make as little as $0 or as much as $200,000. The four potential customers are making independent decisions, and in each case the probability that OfficeQuip will receive the contract is 0.40. When all the decisions have been made, what is the probability that OfficeQuip will receive none of the contracts? Exactly one of the contracts? Exactly two of the contracts? Exactly three of the contracts? All four contracts? Overall, what is OfficeQuip’s expected profit in this business procurement venture?
March 11th, 2009 at 5:53 am
This is a binomial probability problem, all the trials are independent, and the success probability for each trial is 0.40. So the failure probability is 0.60.
Let X = the number of contracts received
P(X = 0) = C(4, 0) * (.40)^0 * (.60)^4 = .1296
P(X = 1) = C(4, 1) * (.40)^1 * (.60)^3 = .3456
P(X = 2) = C(4, 2) * (.40)^2 * (.60)^2 = .3456
P(X = 3) = C(4, 3) * (.40)^3 * (.60)^1 = .1536
P(X = 4) = C(4, 4) * (.40)^4 * (.60)^0 = .0256
Expected profit = $50,000 times the expected number of contracts received = $50,000 * 4 * 0.40 = $80,000