In a survey of 200 employees of a company regarding their 401(k) investments, the following data were obtained.
150 had investments in stock funds.
78 had investments in bond funds.
60 had investments in money market funds.
46 had investments in stock funds and bond funds.
38 had investments in stock funds and money market funds.
36 had investments in bond funds and money market funds.
24 had investments in stock funds, bond funds, and money market funds.
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.)
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.)
one fund: (90+20+10)/200 = 120/200
no fund: 8/200
To find the probability that an employee of the company had investments in exactly one kind of investment fund, we need to calculate the number of employees who had investments in only one fund and divide it by the total number of employees.
From the given data, we can determine the number of employees who had investments in only one fund:
Employees with investments in stock funds = 150 - (46 + 38 + 24) = 42
Employees with investments in bond funds = 78 - (46 + 36 + 24) = 28
Employees with investments in money market funds = 60 - (38 + 36 + 24) = 42
Now, let's calculate the total number of employees who had investments in only one kind of investment fund:
Total employees with investments in only one fund = 42 + 28 + 42 = 112
The probability that an employee chosen at random had investments in exactly one kind of investment fund is:
Probability = (Number of employees with investments in only one fund) / (Total number of employees) = 112/200 = 0.56
Therefore, the probability that an employee of the company chosen at random had investments in exactly one kind of investment fund is 0.56.
To find the probability that an employee of the company chosen at random had no investment in any of the three types of funds, we need to calculate the number of employees who had no investments in any of the funds and divide it by the total number of employees.
From the given data, we can determine the number of employees who had no investments in any of the funds:
Employees with no investments = Total number of employees - (Employees with investments in stock funds + Employees with investments in bond funds + Employees with investments in money market funds)
= 200 - (150 + 78 + 60)
= 200 - 288
= - 88 (since the value is negative, it means there must be an error in the given data)
Since there is an inconsistency in the data, we cannot calculate the probability of an employee having no investment in any of the three types of funds with the given information.
Please check the data and provide the correct values if possible.