Given that P(A)=aP(A) = aP(A)=a and P(B)=bP(B) = bP(B)=b, state an expression for P(A∪B)P(A \cup B)P(A∪B) in terms of aaa and bbb when: (i) AAA and BBB are mutually exclusive, (ii) AAA and BBB are independent.
In a climate study, let HHH be the event of high humidity and TTT be the event of high temperature. It is found that:
P(H∩T′)=0.22,P(T)=0.30andP(H∣T)=0.6 P(H \cap T') = 0.22, \quad P(T) = 0.30 \quad \text{and} \quad P(H|T) = 0.6 P(H∩T′)=0.22,P(T)=0.30andP(H∣T)=0.6Find the value of: P(H∪T)P(H \cup T)P(H∪T)
P(H∩T)P(H \cap T)P(H∩T)
P(H)P(H)P(H)