Lean Manufacturing class Book: Manufacturing Systems Modeling and Analysis PLEAS

Question

Lean Manufacturing class

Book: Manufacturing Systems Modeling and Analysis

PLEASE TRY TO DO IT STEP BY STEP so I can understand the procedure.

1.2. A library has classified its books into fiction and nonfiction. Furthermore, all books can also be described as hardback and paperback. As an experiment, we shall pick a book at random and record whether it is fiction or nonfiction and whether it rback or hardback. (a) Describe the sample space, i.e., list all outcomes. (b) Describe the event space, i.e., list all events. (c) Define a probability measure such that the probability of picking a nonfiction paperback is 0.15, the probability of picking a nonfiction book is 0.30, and the prob- ability of picking a fiction hardback is 0.65. (d) Using the probabilities from part (c), find the probability of picking a fiction book given that the book chosen is known to be a paperback.

Explanation / Answer

Part (a)

Sample space:

{(Fiction-hardback), (Fiction-paperback), (Non-fiction-hardback), (Non-fiction-paperback)} ANSWER

Part (b)

Let A, B, C and D respectively represent the events that the selected book is Fiction-hardback, Fiction-paperback, Non-fiction-hardback, Non-fiction-paperback. Then, the Event Space consists of A, B, C and D. ANSWER

Part (c)

Given

P(Non-fiction-paperback) = 0.15 ……………………………………………………(1)

P(Non-fiction) = 0.30………….. ……………………………………………………(2)

(1) and (2) =>

P(Non-fiction-hardback) = 0.30 - 0.15 = 0.15 ………………………………………(3)

(2) => P(Fiction) = 1 - 0.30 = 0.70…………………………………………………(4)

Given

P(Fiction-hardback) = 0.65……. ……………………………………………………(5)

(4) and (5) =>

P(Fiction-paperback) = 0.70 - 0.65 = 0.05….. ………………………………………(6)

Thus, the probability measure is:

P(A) = 0.65 [from (5)]

P(B) = 0.05 [from (6)]

P(C) = 0.15 [from (3)]

P(D) = 0.15 [from (1)] ANSWER

Part (d)

(1) and (6) => P(Paperback) = 0.15 + 0.05 = 0.20 ………………………………………(7)

(6) => P(Fiction-paperback) = 0.05….. …………………………………………………(8)

(7) and (8) => out of 20 Paperback books, 5 are fiction books. Thus,

Probability of picking a fiction book given it is a paperback = 5/20 = 0.25 ANSWER

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