Three manufacturing plants, say I, II and III, produce 20, 30 and 50 percent of a company’s output respectively. What is the probability that a randomly-chosen item from the company’s warehouse is defective?

The manager of plant III is very quality conscious and only 1% of the items from that plant are defective. Plants I and II have defective rates of 3% and 5% respectively.

An item is selected at random from the company’s warehouse and found to be defective. What is the probability it was manufactured in plant III?

Answer 1

#(1):"The Reqd. Prob.="3.6%.#

#(2):"The Reqd. Prob.="25/36~~69.44%.#

Let #M_1#=the Event that the Unit is manufactured in Plant I.
#M_2 and M_3# denote Events similar to #M_1#.
Clearly, #P(M_1)=20%=2/10, P(M_2)=3/10, &, P(M_3)=5/10#.
Suppose that, #D# denotes the Event that the chosen Unit is

Defective.

In the usual Notation of Conditional Prob. , then, we are given that,

#P(D/M_1)=1%=1/100, P(D/M_2)=3/100, and, P(D/M_3)=5/100#.
#"Now, (1) : The Reqd. Prob.="P(D)=sum_(j=1)^(j=3)P(M_j)P(D/M_j)#
#=(2/10)(1/100)+(3/10)(3/100)+(5/10)(5/100)#
#=36/1000=3.6%#.
#"Next, (2) : The Reqd. Prob.="P(M_3/D)#
#={P(M_3nnD)}/(P(D))={P(D/M_3)P(M_3)}/(P(D))#
#={(5/100)(5/10)}/(36/1000)=25/36~~69.44%#.

Enjoy Maths.!

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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