A)
Probability for exactly 2 of 3 type of defects. = P ( A1
A2 ) + P ( A1
A3 ) + P ( A3
A2 ) - 2 P ( A1
A2
A3
)
P ( A1 A2 ) =
P(A1) + P(A2) - P ( A1 U A2 ) = 0.07
P ( A2 A3 ) =
P(A2) + P(A3) - P ( A2 U A3 ) = 0.05
P ( A1 A3 ) =
P(A1) + P(A1) - P ( A1 U A3 ) = 0.09
Probability for exactly 2 of 3 type of defects. = 0.07 + 0.05 + 0.09 - 0.03
= 0.18
B)
Type 1 effect but not type 2 and 3 = P (
A1 A2 ) + P (
A1
A3 ) /
P(A1)
= ( 0.09 + 0.07 )/ 0.31
= 0.5161
Problem #7: A certain system can experience three different types of defects. Let Ai (1 1,2,3)...
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A certain system can experience three different types of defects. Let A (i 1,2,3) denote the event that the system has a defect of type i. Suppose that PLAI) = 0.33. P(A2) = 0.37. P(43) = 0.37, P(A1 UA2) 0.58, P(A1 U A3) 0.63 (a) Find the probability that the system has exactly 2 of the 3 types of defects. (b) Find the probability that the system has a type 1 defect given that it does not have a type...
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