Solution:
Given:
A: The selected household is prosperous
B : the household is educated
P(A) = 0.125
P(B) = 0.237
P( A and B) = 0.077
Part a)
Find: P( Selected household is either prosperous or educated) =........?
That is:
P( A or B) = .........?
P( A or B) = P(A) + P( B) - P( A and B)
P( A or B) = 0.125 + 0.237 - 0.077
P( A or B) = 0.285
Part b)
Draw a venn diagram that shows P( A and B)
Part c)
Find: P( A and B') =.........?
P( A and B') = P(A) - P( A and B)
P( A and B') = 0.125 - 0.077
P( A and B') = 0.048
This event means occurrence of event A but not the event B
that is: selected household is prosperous but not educated.
Part d)
Find:
P( A' and B') = ...........?
Using De'Morgans Law:
P( A' and B') = P( A or B)'
P( A' and B') =1 - P( A or B)
P( A' and B') = 1 - 0.285
P( A' and B') = 0.715
this event means , neither A nor B.
that is: The selected household is neither prosperous, nor educated.
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