Question

D Question 18 A clearance sale table of sports shirts has the following kinds of shirts Medium 14 20 Large 8 15 Small Total 28 Plain Collar Button Down Total 15 34 72 Find the probability it is large, given it has a plain collar 0 .2857 О .8214 ○ .0428 O .3194 O .8066

Answer 1

Solution:

    We are given that following table :

We have to find the probability that it is Large , given that it has a plain collar.

So lets A = Large and B = Plain Collar , then using conditional probability formula:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

$P(A\cap B) = P(Large \: \: and \: \: Plain Collar)$

$P(A\cap B)=\frac{Number \: of\: Shirts \: which \: are \: Large\: and\: Plain\: Collar}{Total\, Shirts}$

$P(A\cap B)=\frac{8}{72}$

and

$P( B)=\frac{Total \: Number \: of\: Shirts \: which \: are \: of \: Plain\: Collar}{Total\, Shirts}$

$P( B)=\frac{28}{72}$

Thus

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

$P(A|B)=\frac{8/72}{28/72}$

$P(A|B)=\frac{8}{28}$

$P(A|B)=0.2857$

Thus first option is correct.