suppose that a table of part counts is generalized as follows conforms supplier

ID: 2955127 • Letter: S

Question

suppose that a table of part counts is generalized as follows

conforms supplier yes no 1 ka kb 2 a b
where a,b,k are positive integers. Let A denote the event thata part is from supplier 1 and let B denote the event htat a partconforms to specifications. Show that A adn B are independevents.
How do you do this?

conforms supplier yes no 1 ka kb 2 a b
where a,b,k are positive integers. Let A denote the event thata part is from supplier 1 and let B denote the event htat a partconforms to specifications. Show that A adn B are independevents.
How do you do this?

conforms supplier yes no 1 ka kb 2 a b

Explanation / Answer

In a 2 by 2 table, there are 3 ways to show independence betweenevents A & B.

Events A and B are independent if you show any of thefollowing:

1. P(A|B) = P(A),

2. P(A&B) = P(A)* P(B), or

3. P(A|B) = P(A|not B)

We will use the 3rd way to show independence between events A& B.

Conform

not B:

Not conform

Supplier 1

k(a + b)

not A:

Supplier 2

a + b

(k + 1)a

(k + 1)b

P(A|B) = ka / (k + 1)a = k / (k + 1)

P(A|not B) = kb / (k + 1)b = k / (k + 1)