Given p(A)=0.3 p(B)=0.8
P(AUB)=P(A)+P(B)-P(AnB)
As sum of P(A) and P(B) is greater than one so it's clear P(AnB) !=0 and also P(AUB)<=1 --1
P(A) +P(B)=1.1
so minimum value of P(AnB)=0.1 --to get the maximum value of P(AuB)=1
And maximum value of P(AnB) will be when either of A or B is subset of other as P(A)<P(B) so A is subset of B thus P(AnB)=0.3 (maximum value)
Using this maximum value we will get the minimum value of P(AuB)=0.8
So option a is correct.