# A group consists of 12 persons, of which 3 are extremely patient,

Question:

A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person form the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is

(i) extremely patient

(ii) extremely kind or honest. Which of the above you prefer more.                                                                     [CBSE 2013]

Solution:

Number of persons in the group = 12

∴ Total number of outcomes = 12

(i) Number of persons who are extremely patient = 3

So, the favourable number of outcomes are 3.

$\therefore \mathrm{P}$ (selecting a person who is extremely patient) $=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{3}{12}=\frac{1}{4}$

(ii) Number of persons who are extremely honest = 6

Number of persons who are extremely kind = 12 − (3 + 6) = 3

∴ Number of persons who are extremely kind or honest = 6 + 3 = 9

So, the favourable number of outcomes are 9.

$\therefore \mathrm{P}($ selecting a person who is extremely kind or honest $)=\frac{\text { Favourable number of outcomes }}{\text { Total number of outcomes }}=\frac{9}{12}=\frac{3}{4}$