Question

Forty-two percent of a corporation's blue-collar employees were in favor of a modified health care plan, and 22% of its blue-collar employees favored a proposal to change the work schedule. Thirty-four percent of those favoring the health care plan modification favored the work schedule change. What is the probability that a randomly selected blue-collar employee is in favor of both the modified health can plan and the changed work schedule? What is the probability that a randomly chosen blue-collar employee is in favor of at least one of the two changes? What is the probability that a blue-collar employee favoring the work schedule change also favors the modified health care plan?

Answer 1

Answer:

a) 14.28%

b) 49.72%

c) 61.94%

Step-by-step explanation:

In favor of a modified health care plan = 0.42

In favor of a proposal to change the work schedule = 0.22

In favor of both = 0.42*0.34 = 0.1428

a) What is the probability that a randomly selected blue-collar employee is in favor of both the modified health can plan and the changed work schedule?

Since 34% of those in favor of a modified health care plan are in favor of changes to work schedule, the probability of an employee being in favor of both is 0.1428 or 14.28%.

b) What is the probability that a randomly chosen blue-collar employee is in favor of at least one of the two changes?

$P (at\ least\ one) = P(A) + P(B) - P(A\ and\ B)\\P (at\ least\ one) = 0.42+0.22-0.1428 = 0.4972 =49.72\%$

c) What is the probability that a blue-collar employee favoring the work schedule change also favors the modified health care plan?

$P( A|B) =\frac{P(B\cap A)}{P(B)} = \frac{0.1428}{0.22} \\P( A|B) = 0.6491 =61.94\%$

Answer 2

Probability that selected employee is in favor of both the modified health can plan and the changed work schedule is 0.1428

Probability:

Given that;

Employees favor of a modified health care plan = 42%

Employees favor proposal to change the work schedule = 22%

Employees favoring the health care plan modification favored the work schedule change = 34%

Find:

1. Probability that selected employee is in favor of both the modified health can plan and the changed work schedule
2. Probability that chosen employee is in favor of at least one of the two changes
3. Probability that employee favoring the work schedule change also favors the modified health care plan

Computation:

Probability that selected employee is in favor of both the modified health can plan and the changed work schedule = 0.42 × 0.34

Probability that selected employee is in favor of both the modified health can plan and the changed work schedule = 0.1428

Probability that chosen employee is in favor of at least one of the two changes = [0.42 - 0.1428] + [0.22 - 0.1428] + [0.1428]

Probability that chosen employee is in favor of at least one of the two changes = 0.4972

Probability that employee favoring the work schedule change also favors the modified health care plan = 0.1428 / 0.22

Probability that employee favoring the work schedule change also favors the modified health care plan = 0.6490

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