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2.10
(a) The event “both subcontractors will be available” =
AB
, hence
since
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
) 
P
(
AB
)
⇒
P
(
AB
) =
P
(
A
) +
P
(
B
) 
P
(
A
∪
B
)
= 0.6 + 0.8  0.9 =
0.5
(b)
P
(B is available
⏐
A is not available) =
P
(
B
⏐
A
)
=
PBA
PA
()
while it is clear from the following Venn diagram that
=
P
(
B
) 
P
(
AB
).
A
AB
B
A
Hence
(
)
=
P B
P AB
(
)
−
−
1
= (0.8  0.5)/(1  0.6)
= 0.3/0.4 =
0.75
(c)
(i) If A and B are s.i., we must have P(B
⏐
A) = P(B) = 0.8. However, using Bayes’ rule,
P(B
⏐
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This note was uploaded on 04/25/2010 for the course MAE 213 taught by Professor Seshadri,k during the Spring '08 term at UCSD.
 Spring '08
 Seshadri,K

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