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] = 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 %
