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.

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 First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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?

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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:

$P (A) = 0.70, P (P 2) = 0.60, P (A | P 1) = 0.75, P (B | P 1) = 0.25, P (B | P 2) = 0.20$

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