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Probability Theory Sample Assignment

Question: A shopkeeper’s buys a particular kind of lights bulb from these manufacturers A₁, A₂ and A₃. He buys 30% of his stock from A₁, 45% from A₂ and 25% from A₃. In the past he has found that 2% of A₃’s bulb are faulty whereas only 1% of A₁’s is and A₂’s are. Suppose that he chooses a bulb and finds it is faulty. what is the probability that it was one of A₃’s bulb?

Sol: Here P(A₁), P(A₂) and P(A₃) are prior probability because they exist before we gain any information from the experiment itself. If he picks a bulb at random.

P (A₁) = 0.3 P (A₂) = 0.45 & P (A₃) = 0.25
The probability of faulty bulb will be grater than P (A₃) = 0.25. Since A₃ produces a greater proportion of faulty bulbs than A₁ & A₂. If F is the event that the bulb is faulty, then P (A₃/F) is the probability that we require. We have
P (F/A₁) = .01, P (F/A₂) = .01 P (F/A₃) = .02

This information is shown on a tree diagram.



P (A₃/F) =             P (A₃) P (F/A₃)        ____________   
        P (A₁) P (F/A₁) + P (A₂) P (F/A₂) + P (A₃) P (F/A₃)

by using Barye’s The. P (B₁/A) =



=_      _____.25 x .02  ____       = 0.4
    .3 x .01 + .45 x .01 + .25 x .02

Similarly, if we wish to know the probability that the faulty bulb was supplied by A1 or A2, we have

P (A₁/F) =__                 P(A₁)    P(F/A₁)           _____________
             P (A₁) x P (F/A₁) + P(A₂) x P (F/A₂) + P (A₃) x P (F/A₃)
=_______    .3 x .01__  ____      = 0.24
  .3 X .01 + .45 X .01 + .25 x .02

and since A₁, A₂ and A₃ are mutually exclusive
P(A₂/F) = 1-0.4-0.240 = .36

Other Sample Assignments in Statistics Homework Assignment :

Continious Distribution	Descrete Distributions
Descriptive Statistics	Nonparamatric Statistics
Probability	Sampling And Sampling Distribution
Statistical Inference Estimation For Single Popula	Simple Regression Analysis
Statistical Inference About 2 Population	Time Series Forcasting Index Number
Statistical Quality Control	Correlation
Index Number	Larger Sample Mean Proportions
Non Parametric Test	Probability Theory
Sampling Distribution	Simple and Multiple Linear Regression Analysis
Unvariate Analysis

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