Question

Suppose that start-up companies in the area of biotechnology have probability 0.2 of becoming profitable, and that those in the area of information technology have probability 0.15 of becoming profitable. A venture capitalist invests in one firm of each type. Assume the companies function independently

a. What is the probability that both companies become profitable?
b. What is the probability that neither company becomes profitable?
c. What is the probability that at least one of the two companies become profitable?

Answer 1

a) 0.03

b) 0.68

c) 0.32

Explanation:

We are given the following in the question:

B: companies in the area of biotechnology

I: companies in the area of information technology

P(B) = 0.2

P(I) = 0.15

The two events are given to be independent.

a) P(both companies become profitable)

`P(B\cap I) = P(B)* P(I)\\= 0.2* 0.15 = 0.03`

0.03 is the probability that both companies become profitable

b) P(neither company becomes profitable)

`P(B'\cap I')\\=P(B')* P(I')\\=(1-P(B))(1-P(I))\\=(1-0.2)(1-0.15)\\=0.68`

0.68 is the probability that neither company becomes profitable.

c) P(at least one of the two companies become profitable)

`P(B\cup I) = P(B) + P(I) - P(B\cap I)\\= 0.2 + 0.15 - 0.03\\=0.32`

0.32 is the probability that at least one of the two companies become profitable