1. 7/3/2012
Let D denote the event that an IC is defective
Let DR denote the event that ‘reliable’ test finds the IC to be defective
Given, P(D) = .005 P[DR| D] = 198/200 = 0.99
P [DR| not D] = 8/160 = 0.05
How reliable is Reliable?
P[DR] = P[DR and D] + P[DR and not D]
= P[D] × P[DR| D] + P[not D] × P[DR| not D]
= 0.005 × 0.99 + 0.995 × 0.05 = 0.00495 +0.04975 = 0.0547
P[D| DR] = P[DR and D] / P[DR] = 0.00495/0.0547 = 0.0905
P[not D| DR] = 0.9095
If Reliable finds the IC to be
Same calculation using table
not defective
Events Prior Prob P[DR|..] P[DR and ..] P[..|DR] Events Prior Prob P[not DR|..] P[not DR P[..|not DR]
(iii) (iv) and ..]
(i) (ii) =(i)*(ii) =(iii)/P[DR] (i) (ii) (iii)
D 0.005 0.99 0.00495 P[D| DR] D 0.005 0.01 0.00005 P[D| not DR]
=0.0905 =0.000053
Not D 0.995 0.05 0.04975 P[not D| DR] Not D 0.995 0.95 0.94525 P[not D|
=0.9095 not DR]
=0.999947
Sum 1 P[DR]= Sum 1 P[not DR]=
0.0547 0.9453
Bayes Rule Bayes Rule -- using table
P[ A]× P[B | A] events Prior Prob P[B|Ai] P[BAi] P[Ai|B]
P[ A | B] = P[PA∩]B] =
[B
P[Ai]
(ii)
(iii)
=(i)*(ii)
(iv)
=(iii)/P[B]
P[ A ∩ B] + P[ B ∩ Ac ] A1
(i)
P[A1] P[B|A1] P[A1B] P[A1| B]
A2 P[A2] P[B|A2] P[A2B] P[A2| B]
P[ A]× P[ B | A] Ak P[Ak] P[B|Ak] P[AkB] P[Ak| B]
=
P[ A] × P[B | A] + P[ Ac ]× P[ B | Ac ] Sum 1 P[B]
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2. 7/3/2012
First Can contains 10 marbles: 7 red & 3 blue
Monty Hall Problem
Second Can contains 4 blue & 1 red or
‘Khul Ja SimSim’
• The car is behind one of the 3 doors.
• You select door A.
• Aman Verma (who knows where the car is)
opens door B and shows that this is empty.
1 marble 1 marble
Gives you an option of “switch”.
• Should you stick to your initial choice?
The marble drawn from
the Box is found to be
blue. What is the prob.
P(the marble drawn from the that it came from Can2?
Box is blue)=?
1 marble
Solution to KJSS Will the new product do well?
Combine prior opinion with pilot survey
P(door B is opened P( correct door is P( correct door is
Prior
Correct given you select and door B is given Door B is
Probabi
Door door A and correct opened and you opened and you PRIOR PROB
lity
door is..) selected door A) selected door A) 60%
Will do well = 40% of potential customers will like it
Won’t do well = 20% will like it 40%
A 1/3 1/2 1/6 1/3
B 1/3 0 0 0 Pilot survey: from 25 potential customers
C 1/3 1 1/3 2/3
X like it
Is it easier to find
P[B|A] ?
Want P[will do well | X out of 25 like it]
P(door B is
opened) 1/2 A
B
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