Let `A ,B ,C` be three mutually independent events. Consider the two statements `S_1a n dS_2dot` `S_1: Aa n dBuuC` are independent `S_2: Aa n dBnnC` are independent Then, a. both `S_1a n dS_2` are true b. only `S_1` is true c. only `S_2` is true d. neither `S_1norS_2` is true

Let A ,B ,C be three mutually independent events. Consider the two statements S_1 and S_2 . S_1 : A and BuuC are independent S_2 : A and BnnC are independent. Then,

Let A,B, C be three mutually independent events. Consider the two statements S_(1)and S_(2). {:(S_(1):A and B nnC "are independent.",),(S_(2):A and B nnC "are independent.",):} Then

If A ,B ,C be three mutually independent events, then Aa n dBuuC are also independent events. Statement 2: Two events Aa n dB are independent if and only if P(AnnB)=P(A)P(B)dot

Let Aa n dB be two independent events. Statement 1: If P(A)=0. 4a n dP(Auu barB )=0. 9 ,t h e nP(B)i s1//4. Statement 2: If Aa n dB are independent, then P(AnnB)=P(A)P(B)dot .

Events Aa n dC are independent. If the probabilities relating A ,B ,a n dC are P(A)=1//5, P(B)=1//6; P(AnnC)=1//20 ; P(BuuC)=3//8. Then events a)Ba n dC are independent events b)Ba n dC are mutually exclusive events c)Ba n dC are neither independent nor mutually exclusive events d)Ba n dC are equiprobable

Let a=i^i and consider the following statements S_1: a=e^(-pi/2) , S_2 :The value of sin(In a)-1 , Im(a)+arg(a)=0 Now identify the correct combination of the true statements.

Events Aa n dC are independent. If the probabilities relating A ,B ,a n dC are P(A)=1//5, P(B)=1//6; P(AnnC)=1//20 ; P(BuuC)=3//8. Then (a)events Ba n dC are independent (b)events Ba n dC are mutually exclusive events.(c) Ba n dC are neither independent nor mutually exclusive (d)events Ba n dC are equiprobable

Let A B C be a triangle right-angled at Aa n dS be its circumcircle. Let S_1 be the circle touching the lines A B and A C and the circle S internally. Further, let S_2 be the circle touching the lines A B and A C produced and the circle S externally. If r_1 and r_2 are the radii of the circles S_1 and S_2 , respectively, show that r_1r_2=4 area ( A B C)dot

Let S_1 be the set of all those solutions of the equation (1+a)costhetacos(2theta-b)=(1+a\ cos2theta)"cos"(theta-b) which are independent of a\ a n d\ b and S_2 be the set of all such solutions which are dependent on a\ a n d\ bdot The set S_1a n d\ S_2 are given by