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#### Superior Construction Pte Ltd Solved

Referencing Styles : Open | Pages : 4
Andrew Barnes Completed Orders: 1261 5/5

(a) Probability of winning project A = 0.4

Probability of winning project B = 0.3

i)    Probability of company securing project A or B = P(A) + P(B) – P(A and B) = 0.4 + 0.3 -0.4*0.3 = 0.58

P(A and B) = P(A)*P(B) since these two are independent events.

(ii) Probability of not winning A = 1-P(A) =  1-0.4= 0.6

Probability of not winning B = 1-P(B) = 1-0.3 = 0.7

Probability of not securing project A or project B = P(not securing A) + P(not securing B) –P(not securing both) = 0.6 + 0.7 –(0.6*0.7) = 0.88

b) I do not agree with the statement that mutually exclusive events will be independent events. This is primarily because in case of mutually exclusive events the probability of both the events happening together is zero.

However, for independent events , probability of both the events happening together is equal to the product of the two individual probabilities.

Hence, in independent events, P(A and B) = P(A)*P(B)

The product of two probabilities would be zero only if one of the numbers is zero which is not always the case.

Hence, mutually exclusive events will not be independent in every case and would be true for selected few cases where the probability of one of the events is zero.

Mutually Exclusive Event

Consider a situation where, the company has \$ 10 million funds and is considering investment in two project A and B which both demand an outlay of \$ 10 million. This is an example of a mutually exclusive event since if the company decides to invest in project A, then project B is automatically ruled out and vice versa. Also, the company cannot invest in both projects simultaneously.

Independent Event

Consider a situation where, the company has invested in two unrelated businesses which are under completely different management. The success of these businesses would be independent since they would not rely on the success or failure of each other.

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