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

Let Aa n dB b e two independent events. Statement 1: If (A)=0. 3a n dP(Auu barB )=0. 8 ,t h e nP(B) is 2/7. Statement 2: P(E)=1-P(E),w h e r eE is any event.

Events Aa n dB are such that P(A)=1//2, P(B)=7//12 , a n dP(notAornotB)=1//4. State whether Aa n dB are independents?

Roots of the equation |x m n1a x n1a b x1a b c1|=0 are independent of m ,a n dn independent of a ,b ,a n dc depend on m ,n ,a n da ,b ,c independent of m , na n da ,b ,c

Let two fair six-faced dice A and B be thrown simultaneously. If E_1 is the event that die A shows up four, E_2 is the event that die B shows up two and E_3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ? (1) E_1 and E_2 are independent. (2) E_2 and E_3 are independent. (3) E_1 and E_3 are independent. (4) E_1 , E_2 and E_3 are independent.

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 Aa n dB be two events. Suppose P(A)=0. 4 ,P(B)=p ,a n dP(AuuB)=0. 7. The value of p for which Aa n dB are independent is a. 1//3 b. 1//4 c. 1//2 d. 1//5