Of 500 employees, 200 participate in a company's profit sharing plan(P), 400 have major insurance coverage(M), & 150 employees participate in both programs. Construct a Venn diagram and find out the probability that a randomly selected employees a) will be a participant in at least one of two programs b)Will not be a participant in either program
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To construct the Venn diagram, we can start by drawing two overlapping circles to represent the two programs: profit sharing plan (P) and major insurance coverage (M).
Let's label the overlapping region where the two circles intersect as "P and M," which represents the employees who participate in both programs.
Next, we fill in the remaining areas with the number of employees who participate in each program but not both.
- In the region labeled "P," write 200 (since 200 employees participate in the profit sharing plan).
- In the region labeled "M," write 400 (since 400 employees have major insurance coverage).
Lastly, label the part outside of both circles as "Neither P nor M," which represents the employees who do not participate in either program.
Now, let's answer the given questions:
a) To find the probability that a randomly selected employee will be a participant in at least one of the two programs, we need to find the total number of employees in the regions "P," "M," and "P and M" and divide it by the total number of employees (500).
The number of employees in the regions "P," "M," and "P and M" is:
P = 200
M = 400
P and M = 150
Total = P + M - P and M
Total = 200 + 400 - 150
Total = 450
Probability (at least one program) = Total / Total number of employees
Probability (at least one program) = 450 / 500
Probability (at least one program) = 0.9
Therefore, the probability that a randomly selected employee will be a participant in at least one of the two programs is 0.9 or 90%.
b) To find the probability that a randomly selected employee will not be a participant in both programs, we need to find the total number of employees in the region "Neither P nor M" and divide it by the total number of employees (500).
The number of employees in the region "Neither P nor M" is:
Neither P nor M = Total number of employees - (P + M - P and M)
Neither P nor M = 500 - (200 + 400 - 150)
Neither P nor M = 50
Probability (neither program) = Neither P nor M / Total number of employees
Probability (neither program) = 50 / 500
Probability (neither program) = 0.1
Therefore, the probability that a randomly selected employee will not be a participant in either program is 0.1 or 10%.
To construct a Venn diagram, we will need to divide the total number of employees into three groups: those who participate in the profit sharing plan, those who have major insurance coverage, and those who participate in both programs.
Let's denote P as the number of employees who participate in the profit sharing plan, M as the number of employees who have major insurance coverage, and X as the number of employees who participate in both programs.
We know that P = 200, M = 400, and X = 150.
Now, to find the number of employees who do not participate in either program (neither P nor M), we can use the formula:
Total employees = P + M - X + Neither
Since the total number of employees is given as 500, we can substitute in the known values:
500 = 200 + 400 - 150 + Neither
Now we can solve for the number of employees who do not participate in either program (Neither):
500 = 450 + Neither
Neither = 500 - 450
Neither = 50
Now, we can construct the Venn diagram:
_______
/ \
/ P \
\ /
\_______/
/ \
/ X \
\ /
\_______/
|
__|__
/ \
/ \
\ M /
\ /
\_____/
In the Venn diagram, P represents the employees participating in the profit sharing plan, M represents those with major insurance coverage, and X represents the employees participating in both programs.
Now, let's find the probability that a randomly selected employee will be a participant in at least one of the two programs:
To find this probability, we need to calculate the total number of employees who participate in either program (P or M or both) and divide it by the total number of employees.
Total participants = P + M - X
Total participants = 200 + 400 - 150 = 450
Probability of randomly selecting a participant in at least one of the programs = Total participants / Total employees
Probability = 450 / 500
Probability = 0.9
Therefore, the probability that a randomly selected employee will be a participant in at least one of the two programs is 0.9, or 90%.
Now, let's find the probability that a randomly selected employee will not be a participant in either program:
To find this probability, we need to calculate the number of employees who do not participate in either program (Neither) and divide it by the total number of employees.
Probability of not participating in either program = Neither / Total employees
Probability = 50 / 500
Probability = 0.1
Therefore, the probability that a randomly selected employee will not be a participant in either program is 0.1, or 10%.
From the 500 employees in company, 200 participate in the company profile sharing scheme (P), 400 employees have medical insurance protection scheme (M) and 200 employees have both scheme
a)Draw a Venn diagram to illustrate the above information
b)What is the probability that the employee chosen at random
i. Participates at least one of the schemes?
ii. Does not participate in any one of the schemes?