In a self-assessment survey 60% persons claimed that they never indulged in corruption 40% persons claimed that they always speak truth and 20% say that they neither indulged in corruption nor tell lic.A person is selected at random out of this group.
Answers
Given : in a self assessment survey, 60 % claimed that they never indulged in corruption, 40 % claimed that they always spoke truth , 20 % said that they neither told lies nor indulged in corruption.
a person is selected at random
To Find : probability that
1) he is either corrupt or tells lies
2)if a person never indulged in corruption, find probability that he/she tells truth
3)if he speaks truth, find probability that he/she claims not to be corrupt
Solution
X = Not Corrupt
Y = Speak truth / Not Lie
P(X) = 0.6
P(Y) = 0.4
P( X ∩ Y) = 0.2
P ( corrupt or tells lies) = 1 - P( X ∩ Y)
= 1 - 0.2
= 0.8
if a person never indulged in corruption probability that he/she tells truth = P( X ∩ Y) / P(X) = 0.6
= 0.2/0.6
= 1/3
if he speaks truth, probability that he/she claims not to be corrupt
= P( X ∩ Y) / P(Y)
= 0.2/0.4
= 1/2
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