SOLUTION: In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained. 127 had investments in stock funds. 97 had investments in bond f

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Question 1118494: In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained.
127 had investments in stock funds.
97 had investments in bond funds.
60 had investments in money market funds.
43 had investments in stock funds and bond funds.
36 had investments in stock funds and money market funds.
36 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.)
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52810) About Me  (Show Source):
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In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained. 
127		had investments in stock funds.
97		had investments in bond funds.
60		had investments in money market funds.
43		had investments in stock funds and bond funds.
36		had investments in stock funds and money market funds.
36		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? 
  

(b) What is the probability that an employee of the company chosen at random had investments in exactly one kind of investment fund? 
  

(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?

Solution 

We are given

S = 127
B =  97
M =  60

SB = 43
SM = 36
BM = 36

SBM = 22.


(c)  Then  

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

                  = 127 + 97 + 60 - 43 - 36 - 36 + 22 = 191

     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 - 191 = 9.

     Thus the answer to the question (c) is  9%2F200 = 0.045.


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

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

   = (43 - 22)  + (36 - 22)  + (36 - 22) = 49.

      Hence, the answer to question (a) is  49%2F200 = 0.245.



(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) = 

    = (127-43 - 36 + 22)  + (97 - 43 - 36 + 22) + (60 - 36 - 36 + 22) = 120. 

      Hence, the answer to question (b) is  120%2F200 = 0.6.

The solution is completed.


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!



22 are all three so that goes in the center. 36 are Stocks and Money Market, but you have already accounted for 22 of those (the ones in the center) so 36 minus 22 = 14 goes in the space common to Stocks and Money Mkt. Calculate the Stocks/Bonds and the Bonds/Money Mkt the same way. Then, add the number that are Stocks/Bonds, the number that are Stocks/Money Mkt, and the number that are all three. Subtract that from the total invested in Stocks to get the number invested ONLY in Stocks. Calculate the only Bonds and only Money Mkt the same way. Add up all of the numbers you have in the chart and subtract from 200 to get the number invested in None (the number not in any of the circles.

The probability of anything is the number of possible successful outcomes divided by the total number of outcomes. The denominator for all three of your questions is 200. And you can count the number of successes for each of the questions as well as I can. The rest is just calculator work.

By the way, you should check all of the numbers that I entered into the chart above. Sometimes I make arithmetic errors, so you would be foolish to trust me.


John

My calculator said it, I believe it, that settles it