Question

Three assembly lines Alpha, Beta, and Gamma make the same power transistor. Each of the assembly lines has its own level of efficiency. Resulting in inventory having 20% of the transistors from Alpha, 50% from Beta, and the remaining 30% from Gamma. Further the probability a transistor from Alpha will be defective is 0.02, a transistor from Beta will be defective is 0.06, and a transistor from Gamma will be defective is 0.04. If a random transistor from inventory is defective, what is the probability it came from Bet

Answer 1

P [ β / Def] = 0,6521 or 65,21 %

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 %