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@ISHAN TOPRE • 09 Sep, 2011
Friends,
I GATE, I have seen that about 10-12 marks come directly from Maths. Out of which Probability and statistics.has a big share.
I am dedicating this thread to for practicing and posting some simple methods for probability problems.

I will be posting the common types of questions which are asked in GATE.

Feel free to make your contributions.

Instruction: NO SPAMMING. SPAMMERS WILL BE BANNED.
-By order-
@ISHAN TOPRE • 09 Sep, 2011 • 1 like Type 1]

A company has three machines A, B, C. They produce 15%, 20% and 65% of identical goods respectively. Out of them the defective pieces produced by each machine are 0.01, 0.03, 0.15.

What is the probability that a defective piece is selected and it is produced by Machine C?
Solution:[TABLE="class: grid, width: 350"]
[TR]
[TD]Machine[/TD]
[TD]A[/TD]
[TD]B[/TD]
[TD]C[/TD]
[/TR]
[TR]
[TD]Probability Of Production P(M)[/TD]
[TD]15/100[/TD]
[TD]20/100[/TD]
[TD]65/100[/TD]
[/TR]
[TR]
[TD]Defects By Each Machine P(D/M)[/TD]
[TD]1/100[/TD]
[TD]3/100[/TD]
[TD]15/100[/TD]
[/TR]
[/TABLE]



We have to find P(M/D)=P(C/D)

We will use Baye's Theorem
P(C/D)= {0.65*0.15)/ {0.15*0.01+0.20*0.03+0.65*0.15}

P(C/D)=13/14
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