Question 1 A production process uses two machines in its daily production. A random sample of 500 items produced was inspected and listed in the table below. Machine Defective Non-defective Machine A 15 285 Machine B

Question 1

A production process uses two machines in its daily production. A random sample of 500 items produced was inspected and listed in the table below.

If an item is selected randomly,

(a) Find the probability that the item is

• defective
• non-defective
• machine A
• machine B
• defective and is produced by Machine B
• non-defective and is produced by Machine A
• defective given that it is produced by Machine B
• non-defective gave that it is produced by Machine

(b) Determine whether

• the events “ Machine A” and “ Defective” are independent.
• the events “ Machine B” and “ Non-defective” are mutually exclusive.

Question 2

A and B are two events such that P(B) = 1/5 , P(B | A) = 1/3 and P(A | B) = 1/2 .

1. Are A and B independent events?
2. Are A and B mutually exclusive events?
3. Find ( ∩ )
4. Find ( ∪ )