Given PA04 PBA03 andPBA02 find a PA b PBA c PB d PA n B e PA

Given P(A)=0.4, P(B|A)=0.3, andP(B\'|A\')=0.2, find

a) P(A\')

b P(B|A\')

c P(B)

d P(A n B)

e P(A|B)

Solution

Ans: Given P(A)=, P(B/A)=0.3, P(B\'/ A\') = 0.2

From this, we can find that p(A and B)/ p(A)= 0.3.....thus, p(A and B)= 0.3*0.4= 0.12

a)p(A\')= 1-p(A)= 1-0.4= 0.6

b) p(B\'/A\') = 0.2 = p(B\' and A\') / p(A\') = p[(A union B)]\' = 0.2*0.6= 0.12

Then, p(A union B)= 1-0.12= 0.88

c) p(B)= ? p(A union B)= 0.88 = 0.4+ p(B)- 0.12= > thus p(B)= 0.60

d) From above we have seen that p(A and B)= 0.12

e) p(A/B)= p(A and B)/ p(B)= 0.12/0.60= 0.2