1 answer

D Question 18 A clearance sale table of sports shirts has the following kinds of shirts...

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

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

Answers

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.

.

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