If `P(A_1) = 0.3`, then `P(A_1^C) =`?

If P(A_1) = 0.2 , P(A_2) = 0.1 and P(A_3) = 0.3 and these events are mutually independent, then what is the value of P(A_1 nn A_2 nn A_3) ?

For any two events A_1 and A_2 , show that P(A_1 cap A_2)lemin{P(A_1),P(A_2)} where min {P(A_1), P(A_2)} is the minimum of P(A_1) and P(A_2) .

For any two events A_1 and A_2 , prove that P(A_1 nn A_2) le min{PA_1),P(A_2)} where min {PA_1),P(A_2)} is the minimum of P(A_1) and P(A_2) .

Show that P(B)>0 , then P(A_1 cup A_2|B) = P(A_1|B) + P(A_2|B)-P(A_1 cap A_2|B) .

Prove that, if A_1 and A_2 are two events, which are not necessarily mutually exclusive then P(A_1 uu A_2) = P(A_1) + P(A_1 nn A_2)

If A_1 , A_2 , A_3 are mutually exclusive and exhaustive, then P(A_1) + P(A_2) + P(A_3) equal______

If tangent at point P(a,b) to the curve x^3+y^3=c^3 meet the curve agins at Q(a_1, b_1) then (a_1)/a +b_1/b=

Suppose a_1, a_2, are real numbers, with a_1!=0. If a_1, a_2,a_3, are in A.P., then (a) A=[(a_1,a_2,a_3),(a_4,a_5,a_6),(a_5,a_6,a_7)] is singular (where i=sqrt(-1) ) (b)The system of equations a_1x+a_2y+a_3z=0,a_4x+a_5y+a_6z=0,a_7x+a_8y+a_9z=0 has infinite number of solutions. (c) B=[(a_1,i a_2),(ia_2,a_1)] is non-singular (d)none of these

If A_1,A_2 be two AM's and G_1,G_2 be the two GM's between two number a and b , then (A_1+A_2)/(G_1G_2) is equal to

Statement 1: if A={2,4,6,},B{1,5,3}w h e r eAa n dB are the events of numbers occurring on a dice, then P(A)+P(B)=1. Statement 2: A_1, A_2, A_3,...... , A_n are all mutually exclusive events, then P(A_1)+P(A_2)+.......+P(A_n)=1.