In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B)
b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find
P(A).
a)
as event A and B are independent
P(A n B)=P(A)*P(B)
hence P(A u B)=P(A)+P(B)-P(A)*P(B)
P(A u B)=P(A)+P(B)*(1-P(A))
P(A u B)=P(A)+P(B)*P(A')
similarly P(A u B)=P(B)+P(B')*P(A)
hence P(A u B)=P(B)+P(B')*P(A)=P(A)+P(B)*P(A')
b)as P(A n B)=P(A)*P(B)'
P(B n C)=0
P(A n C)=P(A)*P(C)
for P(A u B u C)=P(A)+P(B)+P(C)-P(A)*P(B)-P(A)*P(C)
0.9=P(A)+0.5+0.3-P(A)*(0.5+0.3)
P(A)*0.2=0.1
P(A)=0.5
In a sample space, events A and B are independent, events B and C are mutually...
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