Given two events `Aa n dBdot` If odds against `A` are as 2:1 and those in favour of `AuuB` are as 3:1, then a.`1//2lt=P(B)lt=3//4` b. `5//12lt=P(B)lt=3//4` c. `1//4lt=P(B)lt=3//5` d. none of these

Given two events A and B . If odds against A are as 2:1 and those in favour of AuuB are 3:1 , then find the range of P(B)dot

Let Aa n dB be two event such that P(AuuB)geq3//4 and 1//8lt=P(AnnB)lt=3//8. Statement 1: P(A)+P(B)geq7//8. Statement 2: P(A)+P(B)lt=11//8.

If Aa n dB are two events such that P(A)=1/2a n dP(B)=2/3 , then show that (i) P(AuuB)geq2/3 (ii) 1/6lt=P(AnnB)le1/2 (iii) P(Auu B )lt=1/3 (iv) 1/6leP( A uuB)lt=1/2

Let vec a* vec b=0,w h e r e vec aa n d vec b are unit vectors and the unit vector vec c is inclined at an angle theta to both vec aa n d vec bdot If vec c=m vec a+n vec b+p( vec axx vec b),(m ,n , p in R), then a.pi/4lt=thetalt=pi/4 b. pi/4lt=thetalt=(3pi)/4 c. 0lt=thetalt=pi/4 d. 0lt=thetalt=(3pi)/4

Suppose A and B are two events and P(B) = p, P(A) = p^2 where 0 lt p lt 1. If the odds against A are the cubes of the odds against B, then 6p- 1.2 is equal to ______

The circle x^2 + y^2 - 6x - 10y + p = 0 does not touch or intersect the axes and the point (1, 4) is inside the circle, then (A) 0 lt p lt 29 (B) 25 lt p lt 29 (C) 25 lt p lt 35 (D) none of these

If 2+z+z^4=0, where z is a complex number then (A) 1/2 lt|z|lt1 (B) 1/2lt|z|lt1/3 (C) |z|ge1 (D) none of these