Question

20 ball pens are defective among a heap of 144 ball pens. You would like to buy a good pen not bed. The shopkeeper takes out a ball pen at random from these and gives you. What is the probability that:

(i) You will buy that ball pen.

(ii) You will not buy that ball pen.

Answer 1

The total number of ball pens in the heap = 144.

The number of defective pens = 20

The number of fine ball pens 

= 144 – 20 = 124

(i) Let the probability of buying a pen be (A).

∵ We would like to buy a good pen

∴ The number of favourable outcomes of buying a ball pen = 124

Total number of all possible outcomes = 144

∴ P(A) = \(\frac { 124 }{ 144 }\) = \(\frac { 31 }{ 36 }\)

(ii) Let the event of not buying a ball pen be (\(\overline { A }\))

Then P(\(\overline { A }\)) = 1 – P(A)

= 1 – \(\frac { 31 }{ 36 }\) = \(\frac { 5 }{ 36 }\)