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) = 0.8 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?

Answer 1

Answer:

(a) 0.56

(b) 0.06

(c) 0.94

Step-by-step explanation:

P(E1) = 0.7 and P(E2) = 0.8

(a) The probability that both bids are successful is given by the product of the probability of success of each bid:

$P(E1\ and\ E2) = 0.7*0.8=0.56$

(b) The probability that neither bid is successful is given by the product of the probability of failure of each bid:

$P(not\ E1\ and\ not\ E2)= (1-P(E1))*(1-P(E2))\\P(not\ E1\ and\ not\ E2)=0.3*0.2=0.06$

(c) The probability that the firm is successful in at least one of the two bids is given by the sum of the probability of success of each bid subtracted by the probability that both bids are successful:

$P(E1\ or\ E2)=P(E1)+P(E2) - P(E1\ and\ E2)\\P(E1\ or\ E2)=0.7+0.8-0.56\\P(E1\ or\ E2)=0.94$