Suppose PA070 PB050 PAUB080 a find PAnB b find PAUB c find P

Suppose P(A)=0.70, P(B)=0.50, P(AUB\')=0.80

a) find P(AnB)

b) find P(AUB)

c) find P(AlB)

Solution

a) find P(AnB)

Since P(AUB\')=0.80

--> P(A) + P(B\') - P(A and B\') =0.8

--> 0.7 + (1-0.5) - P(A) +P(A and B) =0.8

--> 1.2 - 0.7 + P(A and B) = 0.8

--> 0.5 + P(A and B) =0.8

So P(AnB) = 0.8-0.5=0.3

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b) find P(AUB)

=P(A) + P(B) - P(AnB)

=0.7+0.5-0.3

=0.9

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c) find P(AlB)

=P(A and B)/ P(B)

=0.3/0.5

=0.6