An anti aircraft gun take four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hit the plane is

A machine operates only when all of its three components function. The probabilities of the failures of the first, second and third components are 0.14,0.10 and 0.05 respectively. What is the probability that the machine will fail.

Three persons A,B and C fire a target in turn . Their probabilities of hitting the target are 0.4 , 0.3 and 0.2 respectively . The probability of two hits is

Three persons A,B and C, fire at a target in turn, starting with A. Their probability of hitting the target are 0.4, 0.3 and 0.2, respectively. The probability of two hits is

The probability that a man will hit a target in shooting practise is 0.3 . If he shoots 10 times, the probability that he hits the target , is

Three persons P, Q and R independentlytry to hit a target. If the probabilities oftheir hitting the target are 3/4,1/2 and 5/8 respectively, then the probability that thetarget is hit by P or Q but not by R is:

Find the point in the XY plane which is equidistant from the points (2,0,3) ,(0,3,2) and (0,0,1)

Two groups are competing for the positions of 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 corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.

An enemy plane is flying horizontally at an altitude of 2 km with a speed of 300 ms^(-1) An army man with an anti-aircraft gun on the ground sights hit enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600 ms^(-1) . At what angle with the vertical should the gun be fired so as to hit the plane ?

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is (A) 0.06 (B) 0.14 (C) 7/22 (D) 0.7

Three persons A, B and C shoot to hit a target. If in trials, A hits the target 4 times in 5 shots, B hits 3 times in 4 shots and C hits 2 times in 3 trials. Find the probability that: Exactly two persons hit the target.