A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?  Choose the correct choice from the following answers
A) 564/123  B) 646/458  C) 456/847  D) 175/256  E) 256/175
The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.   So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.   The event of not hitting the target even once is the complement of the event of hitting the target at least once.   The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾   Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256   The probability that he will hit the target at least in one of the four shots=1-81/256   =175/256   Ans: 175/256
<result>D</result>
A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?