Two construction contracts are to be randomly assigned to on

Two construction contracts are to be randomly assigned to one or more of three firms-I. II. and III. A firm may receive more than one contract. Each contract has a potential profit of S90.000. Find the expected potential prefit for firm I. Find the expected potential profit for firms I and II together.

Solution

Firm I    II        III   

COnstructions contracts = 2

Potential profit = 90000

Each firm has a chance to receive a contract as 1/3

Consider firm A

X no of contract received X is binomial with p =1/3 and n =2

Firm A can receive either 0 contract or 1 or 2

x         0            1                2     Total

p      4/9    1/3    2/9    1

xp    0 1/3 4/9 7/9

Expected potential profit = 7/9(90000) = 70000

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Firm I and II together

Let y be the contract received

Y is binomial with p =2/3 and n =2

y 0 1 2

p 1/9    4/9 4/9 1   

xp       0     4/9      8/9    17/9

Hence Expected value for I and II toether = 17/9(90000) =170000