An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane in the first second third, and fourth shot are respectively 0.2, 0.4 0.2 and 0.1. Find the probability that the gun hits the plane.

The probability that a man buying a shirt is 0.2 and that for buying a trouser is 0.3. The probability that he will buy a shirt given that he buys a trouser is 0.4. i. Find the probability that he will buy both a shirt and a trouser ii. Find the probability that he will buy a trouser, given that he buys a shirt.

then image of the point (-1,3,4) in the plane x-2y=0

Two groups are competing for the position on the Board of Directors of a Corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the coresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.

Find the normal vector to the plane 4x + 2y + 3z – 6 =0

A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of 11 steps, he is one step away from the starting point.

The point in the xy-plane which is equidistant from the points (2,0,3),(0,3,2) and (0,0,1) is

Find the equation of the plane which passes through the point (3,4,-1) and is parallel to the plane 2x - 3y + 5z + 7 = 0. Also, find the distance between the two planes.

Let a plane a x+b y+c z+1=0,w h e r ea ,b ,c are parameters, make an angle 60^0 with the line x=y=z ,45^0 with the line x=y-z=0 and theta with the plane x=0. The distance of the plane from point (2,1,1) is 3 units. Find the value of theta and the equation of the plane.

The ratio in which the plane 2x-1=0 divides the line joining (-2,4,7) and (3,-5,8) is