Question

A factory has two machines P and Q for manufacturing an item. Past record shows that machine P produces 60% of the items of the output and machine Q produces 40% of the items of the output. Further 2% of the items produced by machine P and 1% produced by machine Q are defective. All the items produced in a day are put in one stockpile. Based on this information, answer the following questions.
One item is picked at random from the stockpile
a) What is the probability that this item is defective?
b) If the item is defective one, then what is the probability that this item is produced by
machine P?

Answer 1

Answer:

a) Probability that the item picked randomly being defective is, $\frac{2}{125}$

b) Probability of picked defected item is produced by machine P is, $\frac{3}{250}$

Step-by-step explanation:

Let 100 items are produced in one day.

Clearly P produces 60 items

and Q produces 40 items.

Now 2% of items produced by P are defective and 1% of the items produced by Q are defective.

Defective Items from machine P = $\frac{2}{100}$×$60$ = $1.2$ items

Defective Items from machine Q = $\frac{1}{100}$×$40=0.4$ items

Hence, Out of 100 items produced in a day $1.2+0.4=1.6$ items are defective,

a) Probability that the item picked randomly being defective is,

   ⇒ (Number of Defective items produced in one day) ÷ (Total Number of items produced in one day)

   ⇒ = $\frac{1.6}{100} = \frac{2}{125}$

b) Probability of picked defected item is produced by machine P is,

   ⇒  ( Number of defective items produced by machine P in one day) ÷ ( Total Number of items produced in one day)

   ⇒$\frac{1.2}{100}=\frac{3}{250}$