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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?
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 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`
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