Stage Expansion
Probability problem about companies in different states?
Venture capital gave a boost to available funds to companies in the past recent years. According to economic stats, 2,000 venture capital disbursements were made in 1998. Of these, 334 were to companies in California, 490 were to companies in Florida, 217 were to companies in Virginia, and 71 were for companies in Colorado. 35% of the companies receiving funds were in the early stages of development and 25% were in the expansion stage. If you choose one of these companies randomly to learn about how they used the funds:
A. What is the probability the company chosen will be in Colorado?
B. What is the probability the company chosen will not be from one of the four states?
C. Assuming the companies in the early stages of development were evenly distributed across the country, how many Virginia companies receiving venture capital funds were in their early stages?
probability is the ratio of successful outcomes to all possible outcomes
in this case, an outcome is choosing a company
a) prob of choosing a company in colorado =
71/2000 = 0.036 (or 3.6%)
b) prob that the company was not in CA, FL, VA or CO:
these four states account for 1112 of the total; so companies not in one of these four states account for
2000-1112=888 of the total
prob of choosing a company in another state
=888/2000 = 0.444 or 44.4%
c) 35% were in early stages; if these are distributed uniformly, then 35% of VA’s 217 companies were in their early stages, so we expect 0.35×217=75.95 or 76 companies to be in their early stage (we can’t have a fractional number of companies)
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