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 from 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 values you prefer more?

Answer 1

Since the group consists of 12 persons, sample space consists of 12 persons.

∴Total number of possible outcomes = 12

Let A denote event of selecting persons which are extremely patient

∴ Number of outcomes favourable to A is 3.

Let B denote event of selecting persons which are extremely kind or honest.

Number of persons which are extremely honest is 6.

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

∴ Number of outcomes favourable to B = 6 + 3 = 9.

(i) Probability of selecting a person who is extremely patient is given by P(A).

P(A) = `\text{Number of outcome favourable A}/text\{Totalnumber of the possible outcome}=3/12=1/4`

(ii) Probability of selecting a person who is extremely kind or honest is given by P(B)

P(A) = `\text{Number of outcome favourable B}/text\{Totalnumber of the possible outcome}=9/12=3/4`