Q13 of 249 Page 32

A manufacturer has three machine operators A,B and C. The first operator A produces 1% defective items, whereas the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B on the job for 30% of the time and C on the job for 20% of the time. A defective item is produced. What is the probability that it was produced by A?

Let us assume U1, U2, U3 and A be the events as follows:


U1 = choosing Operator A


U2 = choosing Operator B


U3 = choosing Operator C


A = Producing defective item


From the problem:


⇒


⇒


⇒


⇒ P(A|U1) = P(Producing defective item by operator A)


⇒


⇒ P(A|U2) = P(Producing defective item by operator B)


⇒


⇒ P(A|U3) = P(Producing defective item by operator C)


⇒


Now we find


P(U1|A) = P(The defective item is produced by operator A)


Using Baye’s theorem:


⇒


⇒


⇒


⇒


∴ The required probability is .


More from this chapter

All 249 →
11

An insurance company insured 3000 scooters, 4000 cars and 5000 trucks. The probabilities of the accident involving a scooter, a car and a truck are 0.02, 0.03 and 0.04 respectively. One of the insured vehicles meet with and accident. Find the probability that it is a (i) scooter (ii) car (iii) truck.

 12

Suppose we have four boxes A,B,C,D containing coloured marbles as given below:


One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn form box A? box B? box C?

 14

An item is manufactured by three machines A,B and C. Out of the total number of items manufactured during a specified period, 50% are manufacture on machine A, 30% on B and 20% on C. 2% of the items produced on A and 2% of items produced on B are defective and 3% of these produced on C are defective. All the items stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine A?

 15

There are three coins. One is two - headed coin (having head on both faces), another is biased coin that comes up heads 75% of the times the third is also a biased coin that comes up tail 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two - headed coin?