glitterfairy2716 glitterfairy2716

17-09-2017
Mathematics

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If p(a|b) = 0.35, p(b) = 0.75 and p(a) = 0.44 are the events a and b independent ?

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ghanami ghanami

17-09-2017

hello :
note 1 :
p(A|B) = p(A∩B)/ p(B)

note 2 :
A and B independent: p(A∩B) = p(A)×p(B)
calculate : p(A∩B)
p(A∩B) = p(A|B)×p(B)
p(A∩B) = 0.35 ×0.75 = 0.2625
but : p(A)×p(B) = 0.44×0.75 = 0.33
conclusion :
the events A and B are not independent ?

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