A venture capitalist invests in two start-up companies: (1) firm in the field of

Question

A venture capitalist invests in two start-up companies: (1) firm in the field of biotechnology and (2) firm in the area of IT. The biotech firm has probability 0.25 of becoming profitable, and the IT company has probability 0.20 of becoming profitable If these companies function independently, a) What is the probability that both companies become profitable? a) What is the probability that neither company becomes profitable? b) What is the probability that at least one of the two companies become profitable?

Explanation / Answer

If two events A and B are independent then P(A AND B ) = P(A) * P(B)

P(Biotech firm profitable) = 0.25

P(IT company profitable) = 0.20

a)

P( Biotech firm profitable AND IT company profitable) = P(Biotech firm profitable) * P(IT company profitable)

= 0.25 * 0.20

= 0.05

b)

P( Niether company profitable) =1 - P( At least one company profitable)

= 1- [ P(Biotech firm profitable) + P(IT company profitable) - P( Biotech firm profitable AND IT company profitable)]

= 1 - [0.25 + 0.20 - 0.05]

= 1 - 0.40

= 0.60

c)

P( At least one of two company profitable) = 0.40.

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