Conditional probability question

[Spiti]

Need help with q29. I'm getting odd results. The answer is given as 21/37 in Amit sirs key.

[kangkan]

Hi....P(A/b)= P(X>5 inter 3<X <8)/P(3<X<5)..i am getting the top ppart as 21/50 and bottom part as 37/50 hence 21/50....

[Spiti]

X should be taken as discrete random variable right?

[mrittik]

X is not at all discrete....you integrate both ways first function from 0 to 5 and then 2nd one 5 to 10 and the total one is equal to 1.

[Dreyfus]

P(A inter B) = integration of second function from 3 to 8=21/100
P(B) = integration of first function from 3 to 5 + integration of second function from 5 to 8=37/100
P(A conditional upon B)= 21/37

[phelps.phan]

wats the ans for qn 30?? a. not independent??

[Dreyfus]

Yes they aren't independent as P(A inter B) ≠ P(A)*P(B)

[Spiti]

I mistook X to be a discrete random variable. I thought loaves should be taken in integer quantities.