Question

a box p has 1000 items of which 100 are defective another box q has 500 items of which 20 are defective.the items of both the boxes are mixed and one items is randomly taken out.it is found to be defective.what is the probabilty that the items belongs to box p

Answer 1

In box P 100 are defective out of 1000

so,

Probability of drawing defective item from box P

= 100/1000

=1/10

In box Q 20 are defective out of 500

So,

Probability of drawing defective item from box Q

= 20/500

=1/25

Now, The probability that the defective item belonged to Box P

= (1/10) / (1/10 + 1/25)

= (1/10) / (25 +10)/ 250)

=25/35

=5/7

So,

The probability that it belonged to Box P is 5/7