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# I need help with this probability question please

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A group of people were asked whether they prefer soup or salad for lunch. The table shows the probabilities of the results.

 soup no soup total salad 0.2 0.6 0.8 no salad 0.05 0.15 0.2 total 0.25 0.75 1.00

Let A represent having soup and B represent having salad for lunch. Which statement is true?

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(A) Having soup and salad are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .

(B) Having soup and salad for lunch are not independent events because P(A|B)=P(A) and P(B|A)=P(B) .

(C) Having soup and salad for lunch are independent events because P(A|B)≠P(A) and  P(B|A)≠P(B) .

(D) Having soup and salad for lunch are independent events because P(A|B)=P(A) and P(B|A)=P(B) .

Mar 25, 2019

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P(B|A)=  P(A and B)                0.2

_________   =         _____   =  0.8  =  P(B)

P(A)                    0.25

P(A|B)  =    P ( A and B)              0.2

__________ =        ______    = 0.25 =  P(A)

P(B)                       0.8

So

(D) Having soup and salad for lunch are independent events because P(A|B)=P(A) and P(B|A)=P(B) .   Mar 25, 2019