# A group consists of 12 persons, of which 3 are extremely patients, 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 $( 1)$.extremely patient, $( 2)$.extremely kind or honest. which of the above value you prefer more?

Given: A group of 12 persons, 3 of them are extremely patient, 6 are extremely honest and rast of them are extremely kind.

To do: To find the probability of selecting a person who is $( 1)$.extremely patient, $( 2)$.extremely kind and honest.

Solution:

The group consists of 12 persons

Total number of possible outcomes = 12

Let A is the event of selecting persons who are extremely patient.

Number of outcomes favorable to A is 3.

Let B is the event of selecting persons who are extremely kind or honest.

Number of persons who are extremely honest is 6.

Number of persons who are extremely kind is 12 - (6+ 3) = 3 .

Number of outcomes favourable to $\displaystyle B\ =\ 6+3=9$.

$( 1) .$ $P( A) =\frac{Number\ of\ outcomes\ favorable\ to\ A}{total\ number\ of\ possible\ outcomes}$

$=\frac{3}{12}$

$=\frac{1}{4}$

$( 2)$ $P( A) =\frac{Number\ of\ outcomes\ favourable\ to\ B}{total\ number\ of\ possible\ outcomes}$

$=\frac{9}{12}$

$=\frac{3}{4}$

Each of the three values, patience, honesty and kindness is important in one's life
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