An investment adviser for G. Prowe Rice has many clients owning shares of mutual funds. These mutual funds are categorized as Domestic Equity funds, International Equity funds, or Fixed Income funds. A sample of 65 clients of this investment adviser was randomly selected. The following counts were obtained:
. 30 clients in the sample owned Domestic Equity Funds.
. 17 clients owned International Equity funds and Fixed Income funds
. 53 clients owned Domestic Equity or Fixed Income funds
. 27 clients owned exactly 2 types of these mutual funds
. 5 clients in the sample did not own any shares of mutual funds
. 4 clients owned all three types of mutual funds
. 35 clients owned Fixed Income funds
a) Draw a Venn diagram for this information-label with number of clients in each section of the Venn diagram.
b) How many clients owned only Fixed mutual funds?
c) What is the probability that a client owned only Fixed Income mutual funds?
d) What is the probability that a client owned Fixed Income mutual funds? (note---this is NOT the same question as the previous one!)
e) What is the probability that a client did not own any Domestic Equity funds?
f) What is the probability that a client owned International Equity or Domestic Equity funds, but NOT Fixed Income funds?
g) Given that a client owned a Fixed Income fund, what is the probability that the client also owned an International Equity fund?
h) What is the probability that a client owned Fixed Income funds or no mutual funds?
i) Of those clients owning International Equity Funds, what is the probability that the client also owned a Domestic Equity fund?