In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained. 119 had investme
nts in stock funds. 99 had investments in bond funds. 65 had investments in money market funds. 47 had investments in stock funds and bond funds. 33 had investments in stock funds and money market funds. 33 had investments in bond funds and money market funds. 21 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.)
1 answer:
Answer:
Step-by-step explanation:
total: 200 employees of a company
119 had investments in stock funds
99 had investments in bond funds
65 had investments in money market funds
47 had investments in stock funds and bond funds
33 had investments in stock funds and money market funds
33 had investments in bond funds and money market funds
21 had investments in stock funds, bond funds, and money market funds.
See Venn diagram attached
(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.)
Exactly 2 kinds: 26+12+12 = 50
50/200 = 0.25
(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.)
Exactly one kind: 60+40+20 = 120
120/200 = 0.60
(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.)
60+40+20+26+12+12+21=191
200-191 = 9
9/200 = 0.045
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~ Zoey