Question

There are 48 mobile phones in a group out of which 42 are good, 3 are some defective and other 3 are largely defected. Varnika will purchase the mobile phone only when it is good, but a businessman will buy the mobile phone only when there is defective largely. A phone is chosen at random from these. What is the probability that the chosen phone is:

(i) Accepted by Varnika.

(ii) Accepted by businessman.

Answer 1

Total number of mobile phones = 48.

∴ Total number of all possible outcomes = 48

(i) Number of good mobile phones = 42

A mobile phone is chosen at random.

Varnika will buy the mobile phone only when it is good

Let the event that the mobile phone is good be (A).

∴ The number of favourable outcomes for (A) = 42.

⇒ P(A) = \(\frac { 42 }{ 48 }\) = \(\frac { 7 }{ 8 }\)

(ii) The businessman will buy the mobile phone only when it is defected largely.

The number of mobile phones in which are not defected largely 42 + 3 = 45.

Let the event that the mobile is not defected largely be (B).

∴ The number of favourable outcomes for B = 45.

⇒ P(B) = \(\frac { 45 }{ 48 }\) = \(\frac { 15 }{ 16 }\)

Hence, P(A) = \(\frac { 7 }{ 8 }\), P(B) = \(\frac { 15 }{ 16 }\).