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?

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Solution

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 favorable 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 favorable to B = 6+3 = 9.
(i) Probability of selecting a person who is extremly patient is given by P(A).
$P (A) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o A}{T o a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{3}{12} = \frac{1}{4} .$

(ii) Probability of selecting a person who is extremely kind or honest is given by P(B)
$P (B) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o B}{T o a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{9}{12} = \frac{3}{4}$

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