Your company assigned two accident insurance plans (Plan 1 and Plan 2) among the full-time and part-time staffs. There are 70% of full-time staffs in the company and 60% of staffs had been assigned in Plan 2. Given Plan 1, the probability for full-time staff is 0.75 and the probability for part-time staff is 0.25. The company assigned Plan 2 to part-time staffs with the probability of 0.2.

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Your company assigned two accident insurance plans
(Plan 1 and Plan 2) among the full-time and part-time
staffs. There are 70% of full-time staffs in the company
and 60% of staffs had been assigned in Plan 2. Given
Plan 1, the probability for full-time staff is 0.75 and the
probability for part-time staff is 0.25. The company
assigned Plan 2 to part-time staffs with the probability
of 0.2.
a. What is the probability of a full-time staff with Plan
1 accident insurance?
b. What is the probability of a part-time staff with Plan
1 or Plan 2?
c. If two staffs were selected, what is the probability of
both of them assigned with Plan 1?
Expert Solution
Step 1

Let us denote the following events:

P1: Plan 1 accident insurance is assigned.

P2: Plan 2 accident insurance is assigned.

A: The staff is a full timer.

B: The staff is a part timer.

The given probabilities are as follows:

PA=0.70, P(P2)=0.60, P(A|P1)=0.75, P(B|P1)=0.25, P(B|P2)=0.20

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