A construction firm bids on two different contracts. Let E 1 be the event that t

Question

A construction firm bids on two different contracts. Let E1 be the event that the bid on the first contract is successful, and define E2 analogously for the second contract. Suppose that P(E1) = 0.6 and P(E2) = 0.7 and that E1 and E2 are independent events.

(a) Calculate the probability that both bids are successful (the probability of the event E1and E2).

(b) Calculate the probability that neither bid is successful (the probability of the event (not E1) and (not E2

(c) What is the probability that the firm is successful in at least one of the two bids?

Explanation / Answer

Solutions:

a) Contracts are events, which do not exclude each other;
P(E1 and E2) = P(E1)*P(E2) = 0.6*0.7 = 0.42

b) Sum of all chances should be equal to 1; some part of outcomes overlap, so they are subtracted:
1 = P(E1) + P(E2) - P(E1 and E2) + P(0)
P(0) = 1-(0.6+0.7-0.42)
P(0) = 1-0.88 = 0.12

c) Total of both chances:
P(E1 or E2) = P(E1) + (P(E2)
P(E1 or E2) = 0.6+0.7 = 0.13

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