Statistics and probability

• Dec 10th 2007, 06:46 AM
MS BATOOL
Statistics and probability
Suppose an item is manufacture by three machines X, Y and Z. All the three machines have equal capacity and are operated at the same rate. It is known that the percentages of defective items produced by X, Y and Z are 1, 7, and 12 percent respectively. All the items produced by X, Y and Z are put into one bin. From this bin, one item is drawn at random and is found to be defective. What is probability that this item was produced on Y?

i will be very thankful to you ....if anyone can help me.
• Dec 10th 2007, 06:57 AM
Constatine11
Quote:

Originally Posted by MS BATOOL
Suppose an item is manufacture by three machines X, Y and Z. All the three machines have equal capacity and are operated at the same rate. It is known that the percentages of defective items produced by X, Y and Z are 1, 7, and 12 percent respectively. All the items produced by X, Y and Z are put into one bin. From this bin, one item is drawn at random and is found to be defective. What is probability that this item was produced on Y?

i will be very thankful to you ....if anyone can help me.

You need to use Bayes' theorem:

$A$ - sampled item produced by Y
$B$ - sampled item defective

$p(A|B)=\frac{p(B|A)p(A)}{p(B)}$

The data you need to compute this are:

$p(B|A)=0.07$
$p(A)=1/3$
$p(B)=(1/3)\times 0.01 + (1/3)\times 0.07 + (1/3) \times 0.12$

ZB
• Dec 10th 2007, 07:25 AM
MS BATOOL
Thanks
Hi....i want to thank for this most useful and fast reply....once again thanks with regards.:)