33)
Pr(Z<0.5)=1-Pr(Z>0.5)
=1-Pr(X>0.5,Y>0.5) Since if min of 2 is greater than a no. then the other will also be greater than that no.
=1-Pr(X>0.5)Pr(Y>0.5) X and Y are independent
= 1-(1/2)(1/2)
=0.75
34)
Pr(Z<.5|X=.75) = Pr(Y<.5|X=.75) because if X is the minimum then it will be Pr(X<.5|X=.75) which is not possible and will lead to zero so only the other possibility
=Pr(Y<.5)P(X=.75) X and Y are independent
=(1/2)(1)
=.5
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"You don't have to believe in God, but you should believe in The Book." -Paul Erdős
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