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tensa zangetsu [6.8K]
3 years ago
12

Three assembly lines Alpha, Beta, and Gamma make the same power transistor. Each of the assembly lines has its own level of effi

ciency. 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
Mathematics
1 answer:
vova2212 [387]3 years ago
4 0

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 %

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