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CBSE Class 12-science Answered

Probability 
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Asked by alanpeter9611 | 15 Feb, 2019, 06:06: PM
answered-by-expert Expert Answer
Let p(X) be the probability of selecting shop-X and p(Y) be the probabilty of selecting shop-Y
 
p(X) = p(Y) = 1/2
 
probability of getting adulterated ghee from selected shop-X,  = p(A|X) = 40/70 = 4/7

probability of getting adulterated ghee from selected shop-Y = p(A|Y) = 60/110 = 6/11
 
Let p(Y|A) be the probabilty of getting adulterated ghee from shop-Y,  if shop is selected randomly
 
By Baye's theorem,  begin mathsize 12px style p left parenthesis Y vertical line A right parenthesis space equals space fraction numerator p left parenthesis Y right parenthesis space p left parenthesis A vertical line Y right parenthesis over denominator p left parenthesis X right parenthesis p left parenthesis A vertical line X right parenthesis space plus space p left parenthesis Y right parenthesis space p left parenthesis A vertical line Y right parenthesis space end fraction space equals space fraction numerator begin display style 1 half end style cross times begin display style 6 over 11 end style over denominator begin display style 1 half end style cross times begin display style 4 over 7 end style plus begin display style 1 half end style cross times begin display style 6 over 11 end style end fraction space equals space fraction numerator begin display style 6 over 11 end style over denominator begin display style 4 over 7 end style plus begin display style 6 over 11 end style end fraction space equals space 21 over 43 end style
Adulteration is prevented by rigorous checking.
 
Instead of selecting the shop randomly and checking the adulteration by selecting one tin, 
more number of ghee tins should be selected from each shop and should be tested for adulteration.
In later case, probability of finding the adulterated ghee is more.
 
Answered by Thiyagarajan K | 16 Feb, 2019, 03:39: PM

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