A department store carries a deep V female formal dress with

A department store carries a deep V female formal dress with four sizes labeled as S1,S2, S3 and S4, respectively, and four colors labeled as C1. C2, C3 and C4, respectively. The following table lists the numbers of such dresses sold last month. Color Small (St) Medium (S) Large (S3) Extra Large (S4Sum lack (C1) 29 26 39 10 25 25 23 34 23 105 (C2) (C3) 48 15 Total

Solution

a.
P( Blue ) = P( C3 ) = 104/500
P( Extra large ) = P( S4 ) = 170/500
P( Blue and Extra Large) = P( C3 n S4 ) = 27/500

P( Blue OR Extra Large) = P( C3 OR S4 ) = P( C3 ) + P( S4 ) - P( C3 n S4 ) = 104/500 + 170/500 - 27/500 = (104+170-27)/500 = 0.494

b.
Union of the events

c.
P(Black) = P(C1) = 136/500
P( Large ) = P(S3) = 105/500
P( Large and Black) = P( C1 and S3) = 25/500
P( Large given that it is Black) = P( C1 | S3) = P( C1 and S3) / P(S3) = 25/105 = 0.23809