A defective coin minting machine produces coins whose probability of Heads is a random variable Q with PDF

Question

fQ(q)={3q2,0,if q∈[0,1],otherwise.
A coin produced by this machine is tossed repeatedly, with successive tosses assumed to be independent. Let A be the event that the first toss of this coin results in Heads, and let B be the event that the second toss of this coin results in Heads.

P(A)=- unanswered
(Your answer should be a number.)
Find the conditional PDF of Q given event A. Express your answer in terms of q using standard notation.

For 0≤q≤1, fQ∣A(q)=- unanswered
P(B∣A)=- unanswered
(Your answer should be a number.)

Answer 1

a) 0.75

Answer 2

For 0≤q≤1, fQ∣A(q)= 4*q^3

P(B∣A) = 0.8

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Answer 3

a) integral(5*q^4*q,q,0,1) in WolframAlfa=5/6
b)(5*q^4*q)/(5/6)
c=P(B|A)=P(A) independent tosses=5/6