Awarding road contracts. A state Department of Transportation (DOT) recently claimed that each of five bidders received equal consideration in the awarding of two road construction contracts and that, in fact, the two contract recipients were randomly selected from among the five bidders. Three of the bidders were large construction conglomerates and two were small specialty contractors. Suppose 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 an inconsistent with the DOT's claim that the selection was random?

a) Hence, the probability of this event occurring if, in fact, the DOT's claim is true

= 3/10 = 0.3

Step-by-step explanation:

a) The concept applied here is combinatorics; nCr = n! / (n - r) ! r!

we are told that out of 5bidders, Three of the bidders were large construction conglomerates

and two were small specialty contractors.

selecting two recipients with tree of the bidders were large construction conglomerates 3C2

= 3! / (3-2) !2!

= 3

Similarly, selecting the two small casualty contractor from the total of 5bidders = 5C2

= 5! / (5-2) !2!

= 10

Hence, the probability of this event occurring if, in fact, the DOT's claim is true

= 3/10 = 0.3

b) if DOTs claim is not true (probability of failure) = 1 - 0.3

= 0.7, this value implies that the probability 0.3 is largely compatible and a compliment of the 0.7 and as such it is consistent with the DOTs claim that the selection was random.