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Mathematics

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snow_lady [41]3 years ago

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Non existent that is your answer thank you

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4 years ago

Read 2 more answers

Two construction contracts are to be randomly assigned to one or more of three firms: I, II, and III. Any firm may receive both

vichka [17]

Answer:

The owner's total profit is $120,000.

Step-by-step explanation:

Assume that:

X₁ = contract is assigned to firm 1

X₂ = contract is assigned to firm 2

The sample space for assigning the two contracts is:

S = {(I, I), (I, II), (I, III), (II, I), (II, II), (II, III), (III, I), (III, II) and (III, III)}

There are total of 9 possible combinations.

So, the probability of selecting any of the combination is, 1/9.

Compute the probability distribution of X₁ and X₂ as follows:

X₁ P (X₁) X₂ P (X₂)

0 4/9 0 4/9

1 4/9 1 4/9

2 1/9 2 1/9

Compute the expected values of X₁ and X₂ as follows:

$E(X_{1})=\sum X_{1}\cdot P(X_{1})\\\\=(0\times\frac{4}{9})+(1\times\frac{4}{9})+(2\times\frac{1}{9})\\\\=\frac{6}{9}\\\\=\frac{2}{3}$ $E(X_{2})=\sum X_{2}\cdot P(X_{2})\\\\=(0\times\frac{4}{9})+(1\times\frac{4}{9})+(2\times\frac{1}{9})\\\\=\frac{6}{9}\\\\=\frac{2}{3}$