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) = 0.7 and P(E2) = 0.4 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

P(E1) = 0.7

P(E2) = 0.4

a) P (event E1 and E2) = P(E1) * P(E2)

= 0.7 * 0.4

= 0.28

b) The probility that the event E1 is not successful = 1 - 0.7 = 0.3

The probability that the event E2 is not successful = 1 - 0.4 = 0.6

P(the event not E1 and not E2) = P(not E1) * P(not E2)

= 0.3 * 0.6 = 0.18

C) P(successful in at least one of the two bids) = P (succe ss in E1) + P(success in E2) - P( success in E1 and E2)

= 0.7 + 0.4 - (0.7 * 0.4)

= 1.1 - 0.28 = 0.82 (ans)

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