Answer:
P [ β / Def]  = 0,6521   or    65,21 %
Step-by-step explanation:
Tree diagram:
0,20 (α)    Defective  0,02
0,50 (β)    defective  0,06
0,30 (γ)    defective   0,04
According to Baye´s Theorem
P [ A/B] Â = P[A] * P [ B/A] / P[B]
if we call
β = A  and  Defective = B    then  P[β] = P[A]  and P[Defective] = P[B]
we get :
P [ β / Def]  = P[β] * P [ def./β] / P[def]
Then
P[β] = 0,5
P[def/β] = 0,06
P [Defective] = 0,02* 0,2 + 0,06*0,5 + 0,04*0,3
P [Defective] = 0,004 + 0,03 + 0,012
P [Defective] = 0,046
P [ β / Def]  = 0,5 * 0,06 / 0,046
P [ β / Def]  = 0,6521   or    65,21 %