A company sponsors two ventures, that of Smith and Jones, respectively. Assume t

Question

A company sponsors two ventures, that of Smith and Jones, respectively. Assume that Smith's venture has a 70% chance of succeeding, Jones's venture has a 60% chance of succeeding, and that the success of Smith's venture is independent of that of Jones.

                   (a) Determine the probability of Smith's venture failing.

                   (b) Determine the probability of both Smith's and Jones's ventures succeeding.

            (c) Determine the probability of Smith's venture succeeding or Jones's venture succeeding.

            (d) Determine the probability of Smith's venture succeeding, given that Jones's venture succeeds.

Explanation / Answer

Let A denote Smith's venture has succeeding

B denote Jone's venture has succeeding

Given P(A) = 0.70, P(B) = 0.60

a) P(A') = 1 - P(A) = 1 - 0.70 = 0.30

b) P(A and B) = P(A) P(B) since A and B are independent

= 0.70*0.60 = 0.42

c) P(A or B) = P(A) + P(B) - P(A and B)

= 0.70 + 0.60 - 0.42 = 0.88

d) P(A/B) = P(A and B) / P(B) = 0.42 / 0.60 = 0.7

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