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\centerline{Mathematics 375 -- Probability and Statistics 1}
\centerline{Discussion 2 -- The ``Event-Composition Method''}
\centerline{September 17, 2009}
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{\it Background}
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The idea of the event-composition method
is to recognize that the event of interest $E$
can be defined using some combination of 
unions, intersections, or complements of other known
events.  Then apply the additive and multiplicative
laws of probability:
$$P(A\cup B) = P(A) + P(B) - P(A\cap B)$$
and 
$$P(A \cap B) = P(A)P(B|A) = P(B)P(A|B)$$
to find $P(E)$ from the other given information.
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{\it Discussion Questions}
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A)  Given: $P(A) = .2$, $P(B) = .3$, $P(A\cup B) = .4$.  Determine:
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\item{1)} $P(\overline{A} \cup \overline{B})$.
\item{2)} $P(\overline{A} | B)$.  
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B)  The circles marked 1,2,3,4 in the following diagrams
represent electrical relays that operate
independently and function properly with probability $p = .85$.
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Which design yields the higher probability that
current will flow when the relays are activated?
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C)  An accident victim will die unless he receives type 
$A+$ blood before 10 minutes elapse.  He will be saved if
he does get the blood transfusion.  
Potential donors and a reusable blood typing kit are available, 
but it takes 2 minutes to determine each donor's blood type, 
and only $40\%$ of them have type $A+$ blood. 
What is the probability that the victim will be saved
if only one donor's blood can be typed at a time?
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\noindent
{\it Assignment}
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Group writeups due Monday, September 21.
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