A state Department of Transportation DOT recently claimed th

A state Department of Transportation (DOT) recently claimed that each of five bidders recieved equal consideration in the awarding of two road construction contrcts and that, in fact, the two contract recipients were randomly selected from among the five bidders. Three of the bidders were larger construction conglomerates and two were small speciality contractors. Supposed that both contracts were awarded to large construction conglomerates.

a.) What is the probability of this event occurring if, in fact, the DOT\'s claim is true?

b.) Is the probability computed in part a inconsistent with the DOT\'s claim that the selection was random?

Solution

a)

There are 5C2 = 10 ways to choose any two bidders.

There are 3C2 = 3 ways to choose any two large bidders.

Thus,

P(both large) = 3/10 or 0.3 [ANSWER]

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b)

Yes, because the probability in part A is not a rare event. (Greater than 0.1)