" Simplify: "((p^(a+b))^(5)*(p^(b+c))^(5)*(p^(c+a))^(5))/((p^(a)*p^(b)*p^(c))^(10))

Simplify (p^(a)/p^(b))^(c)xx(p^(b)/p^(c))xx(p^(c)/p^(a))

[P^((b-c))]^(b+c)*[P^((c-a))]^(c+a)*[P^((a-b))]^((a+b))=?

The expression ((log_((a)/(b))p)^(2)+(log_((b)/(c))p)^(2)+(log_((a)/(a))p)^(2))/(((log_((a)/(b))p+log_((b)/(c))p+log_((c)/(a))p))^(2)) wherever defined,simplifies to

Let 0ltP (A)lt1, 0ltP(B) lt1 and P(A uu B)=P(A)+P(B)-P(A)*P(B) then (A) P(B//A)=P(B)-P(A) (B) P(A^(c)-B^(c))-P(A^(c))-P(B^(c)), (C) P(A uu B)^(c)=P(A^(c))*P(B^(c)) (D) P(A//B)=P(A)

If A, B are two events, then show that (i) P((A)/(B))P(B)+P((A)/(B^(C )))P(B^(C ))=P(A) (ii) P(A^(c )|B^(c ))=(1-P(AuuB))/(1-P(B)),P(A) gt 0, P(B) ne 1 (iii) P(A//B^(C ))=(P(A)-P(AnnB))/(-P(B)),P(B^(C )) gt 0

For any two events A,B shows that P(AcapB)-P(A)P(B)=P(A^(C))P(B)-P(A^(C)capB) =P(A)P(B^(C))-P(AcapB^(C))

For positive real numbers a ,bc such that a+b+c=p , which one holds? (a) (p-a)(p-b)(p-c)lt=8/(27)p^3 (b) (p-a)(p-b)(p-c)geq8a b c (c) (b c)/a+(c a)/b+(a b)/clt=p (d) none of these