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 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//6. Statement 2: If Aa n dB are independent, then P(AnnB)=P(A)P(B)dot.

If S_1, S_2, S_3 are the sums to n, 2n, 3n terms respectively for a GP then prove that S_1,S_2-S_1,S_3-S_2 are in GP.

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

Consider the following statements : S_(1) : If A={a} and B = {a, b, c}, then A in B . S_(2) : If n(A)=x, then n(P(A))=2^(x) . S_(3) : (AuuB)sube A . S_(4) : phi is subset of every set State, in order, whether S_(1), S_(2), S_(3), S_(4) and true or false

Which of the following is not true for S_(N^(1)) reaction ?