Consider the Cartesian plane `R^(2)` and let `X` denote the subset of points for which both coordinates are integer. A coin of diameter `1//2` is tossed randomly onto the plane. The probability `p` that the coin covers a point of `X`

Find the probability distribution of a random variable X which denotes the number of tails in two tosses of a coin.

the point lies in half plane x-2y<0 as

In a cartesian plane x - coordinate of a points is called _________ .

Consider a plane x+y-z=1 and point A(1, 2, -3) . A line L has the equation x=1 + 3r, y =2 -r and z=3+4r . The coordinate of a point B of line L such that AB is parallel to the plane is

Consider the points A(0,1)a n dB(2,0),a n dP be a point on the line 4x+3y+9=0 . The coordinates of P such that |P A-P B| is maximum are

In R^3 , consider the planes: P_1: y=0 and P_2:x+z=1 . Let P_3 be a plane, different from P_1 and P_2 , which passes through the intersection of P_1 and P_2 . If the distance of the point (0,1,0) from P_3 is 1 and the distance of a point (alpha, beta, gamma) from P_3 is 2, then which of the following relations is (are) true?

Find the ratio in which the plane x-2y+3z=17 divides the line joining the points (-2,4,7) and (3,-5,8). Also obtain the coordinates of the point of intersection.

A coin is tossed 4 times. Let X denote the number of heads. Find the probability distribution of X, its mean and variance.

A coin is tossed twice. Let X denotes of the number of times 'head' tunrs up. Write down the probability distribution of X.