Question

In a survey of 99 families in Karachi, 45 were low income families who at some point in time were involved in electricity theft. 13 were low income families who never did any violation. 16 were high income families who involved in electricity theft, and 25 high income families never did any violation.

If One of these subject is randomly selected, what is the probability of:

i. Low income families or someone who did electricity theft.

ii. Low income families or someone who did not do violation.

iii. High income families or someone who did electricity theft.

Answer 1

Using the formula of P (A B) = P(A) + P(B) - P(A B) i.e. in the question 'or' represents

i) P( Low income families or someone who did electricity theft ) = P( Low income families ) + P(someone who did electricity theft) - P( Low income families and someone who did electricity theft )
=   +   --
= 0.747475

ii) P ( Low income families or someone who did not do violation.) = P( Low income families ) + P(someone who did not do electricity theft) - P ( Low income families and someone who did not do violation.)
=   +   --
= 0.838384

iii) P( High income families or someone who did electricity theft ) = P( High income families ) + P(someone who did electricity theft) - P( High income families and someone who did electricity theft )

= + --
= 0.86869

Hope this answers your query!