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Probability if P(A) = 0.6 P(A/B) = 0.5 FIND P(A’/B’) ?

Probability
if P(A) = 0.6   P(A/B) = 0.5  FIND P(A’/B’) ?

Grade:10

1 Answers

Shravan
27 Points
4 years ago
Since A and B are two events
As P(A)=0.6 then P(B) = 1-P(A) = 1-0.6=0.4
Now P(A’/B’)=P(A’^B’)/P(B’) = P(AUB)’/[1-P(B)]
= 1-P(AUB)/1-P(B)           ----(1)
next given that P(A/B) = 0.5
Also we know that P(A/B) = P(A^B)/P(B) 
0.5=P(A^B)/0.4
So we get P(A^B) as 0.5×0.4=0.2   
now P(AUB) = P(A)+P(B)-P(A^B)
= 0.6+0.4-0.2
=0.8   put this value in (1)
so we get P(A’/B’) = 1-0.8/1-0.4 which is 0.2/0,6 = 1/3=0.33
 so required answer is 0.33
                                            

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