Question

In: Statistics and Probability

In a survey of 200 employees of a company regarding their 401(k) investments, the following data...

In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained.

131		had investments in stock funds.
92		had investments in bond funds.
67		had investments in money market funds.
49		had investments in stock funds and bond funds.
34		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.)

Expert Solution

We are given

S = 131

B = 92

M = 67

SB = 49

SM = 34

BM = 35

SBM = 22.

(a)  The number of those who had investments in exactly two kinds of investment funds is

     (SB - SBM) + (SM - SBM) + (BM - SBM) =

(49 - 22) + (34 - 22) + (35 - 22) = 52

Hence, the answer to question (a) is = 52/200 = 0.260

(b)  The number of those who had investments in exactly one kind of investment fund is

(S - SM - SB + SBM) + (B - SB - BM + SBM) + (M - SM - BM + SBM) =

(131 - 34 - 49 + 22) + (92 - 49 - 35 + 22) + (67 - 34 - 35 + 22 ) = 120

Hence, the answer to question (b) is  120/200 = 0.60.

(c)  Then  

     n(S U B U M) = S + B + M - SB - SM - BM + SBM =

=131+92+67-49-34-35+22 = 194

is the number of those  who had investment at least in one of the three types of funds.

     Hence, the number of those who had NO investment in any of the three types of funds was 200 - 194 = 6

Thus the answer to the question (c) is 6/200 = 0.030

orchestra answered 2 years ago

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