Question

		Edge	Finish
		Excellent	Good
Surface	Excellent	77	1
Finish	Good	2	20

Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 100 parts are summarized as follows

Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish. Determine the number of samples in each of the following events.

(a) A' n B

(b) B'

(c) A U B

Answer 1

Answer

First,we have to find the samples in event A and event B

Event A include excellent surfce finish, so this include 1 sample because only 1 sample qualify as excellent surface finish

Event B include excellent edge finish, so this include 2 sample because only 2 samples qualify as excellent edge finish

we have total 100 samples

(a) A' means compliment of A, i.e. all samples excluding A's sample. So, A' inlcude 100-1 = 99 samples

Now, we have to find the intersection of A' and B. Intersection of A' and B will include only those samples which are same or common in both event A' and B.

So, there will be only 2 samples which are in A' as well as in B

So, we can write it as

(b) B' means compliment of B, i.e. all samples excluding B's sample. So, B' inlcude 100-2 = 98 samples

So, we can write B' = 98 samples

(c) A union B or means all the samples which are included in A and B

AUB

we have 1 sample in event A and 2 samples in event B

So, we can write it as

= 3

AUB