Question

1. In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained. 122 had investments in stock funds. 102 had investments in bond funds. 68 had investments in money market funds. 49 had investments in stock funds and bond funds. 35 had investments in stock funds and money market funds. 35 had investments in bond funds and money market funds. 22 had investments in stock funds, bond funds, and money market funds. (a) What is the probability that an employee of the company chosen at random had investments in exactly two kinds of investment funds? (Enter your answer to three decimal places.) (b) What is the probability that an employee of the company chosen at random had investments in exactly one kind of investment fund? (Enter your answer to two decimal places.) (c) What is the probability that an employee of the company chosen at random had no investment in any of the three types of funds? (Enter your answer to three decimal places.)

2. Let S = {b, e, m, q, u, x} be a sample space of an experiment and let E = {b, e} and F = {b, q, x} be events of this experiment. (Enter ? for the empty set.) Find the events E ? F and E ? F. E ? F = E ? F =

Answer 1

1) Let, A be the event "employees had investments in stock funds"

B be the event "employees had investments in bond funds"

C be the event "employees had investments in money market funds"

Then, A = 122

B = 102

C = 68

  

  

  

  

a) The probability that an employee of the company chosen at random had investments in exactly two kinds of investment funds is = [(35-22)+(35-22)+(49-22)]/200 = 53/200 = 0.265

b) The probability that an employee of the company chosen at random had investments in exactly one kind of investment fund is = [{122-(35+49)+22}+{102-(49+35)+22}+{68-(35+35)+22}]/200 = 120/200 = 0.6

c) The probability that an employee of the company chosen at random had no investment in any of the three types of funds is = [200-(120+53+22)]/200 = 5/200 = 0.025

2) Given S = {b,e,m,q,u,x}, E = {b,e}, F = {b,q,x}

Then, = {b,e,q,x}.

And, = {b}.