Agroup of people were given a personality test to determine if they were type a or type b. the results are shown in the table below.

male female
type a 55 75
type b 48 22

compare p(male | type b) with p(male or type b).
p(male | type b)> p(male or type b)

p(male | type b)< p(male or type b)

p(male | type b) = p(male or type b)

there is not enough information.

             Male Female
Type A  55      75
Type B  48      22

Compare P(Male | Type B) with P(Male or Type B).

P(Male | Type B) = [number of male people inside the type B]  / [number of Type B people] =

= 48 / (48 + 22) = 48 / 70 = 24/35 = 0.686

 P(Male or Type B) = [number of male + number of type B - number that aree both] / total population = [103 + 70 - 48] / 200 = 125 / 200 = 0.625

Then,  P(Male | Type B)> P(Male or Type B)

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