Conditional Probability Question

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Hi i'm having trouble doing this question, any help would be much appreciated

The time needed to defuse the bomb is modeled by a continuous uniform random variable A in the interval (0,2) The the lifetime of the bomb is modeled by a random variable B. Given A=a its assumed that B has a moment generating function 1/(1-at) (0<a<2)

1.What is the expected time he needs to finish defusing the bomb?
2.What is E[B|A] and Var [B|A]
3.What is E and Var


for 1. i it would be .5(0+2)= 1
for 2. i don't really know what to do???
for 3. i think i would just use the law of total probability E[Pr(B|A)] but not sure if that's right though

Thank you in advance!!

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