Homework 2

	Student A
Full Name	Ido Fang Bentov
ID	CLASSIFIED
Email	CLASSIFIED

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Question 1

An item is purchased from three different suppliers. The probability of an item purchased from supplier being defective is , the probability of an item purchased from supplier being defective is , and the probability of an item purchased from supplier being defective is . A bin contains items from supplier , items from supplier and items from supplier .

Part a

What is the probability that an item randomly selected from the bin is defective?

Solution:
The probability of selecting an item from a specific supplier is:

Denoting a item being defective as , we know that:

Therefore, using the total probability rule:

We get:

Part b

If one item randomly selected from the bin is defective, then what is the probability that the item was purchased from Supplier ?

Solution:
Using bayes’ rule:

We get: