of 500 employees, 200 participate in a company's profit- sharing plan (P), 400 have major-medical insurance coverage (M). and 150 employees participate in both programs. Construct a Venn diagram and find out the probability that a randomly-selected employees will be a participant in at least one of the two programs
To construct a Venn diagram, we will need to represent the three sets: participants in the profit-sharing plan (P), employees with major-medical insurance coverage (M), and those who participate in both programs (P∩M).
Based on the given information, we have:
P = 200 (participants in the profit-sharing plan)
M = 400 (employees with major-medical insurance coverage)
P∩M = 150 (participants in both programs)
Now, let's calculate the number of employees who are not participants in either program. To do this, we subtract the number of employees who are in both programs from the total number of participants in each program:
Number of employees not in any program = Total employees - (P + M - P∩M)
Total employees = 500
P = 200
M = 400
P∩M = 150
Number of employees not in any program = 500 - (200 + 400 - 150) = 50
Now we can construct the Venn diagram:
P P∩M
| |
| |
|_______|
M
Label the values on each section of the diagram:
P = 200
P∩M = 150
M = 400
Not in any program = 50
To find the probability that a randomly-selected employee will be a participant in at least one of the two programs, we need to calculate the ratio of the number of employees in the union of the two sets (P∪M) to the total number of employees:
Probability = (P∪M) / Total employees
For a Venn diagram, P∪M can be calculated as:
P∪M = P + M - P∩M
P = 200
M = 400
P∩M = 150
P∪M = 200 + 400 - 150 = 450
Now we can calculate the probability:
Probability = (P∪M) / Total employees = 450 / 500 = 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%.