Answers
below is pmf of X:
P(X=1)=P(first deck contains the card John is looking for) =1/5
P(X=2)=P(first deck not but second deck contain the card) =(4/5)*(1/5)=4/25
P(X=3)=P(first 2 deck not contains but third pack contains)=(4/5)2*(1/5)=16/125
P(X=4)=P(first 2 deck not contains but third pack contains)=(4/5)3*(1/5)=64/625
P(X=5)=P(first 4 pack not contains)=(4/5)4 =256/625
hence P(X>=3) =P(X=3)+P(X=4)+P(X=5)=(16/125)+(64/625)+(256/625)=400/625=16/25
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