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?

• probability to hit a target is 1/4 and probability to miss it is 1-1/4=3/4
  probablity to hit in four sucessions=1-(3/4)^4=175/256
• 12 years agoHelpfull: Yes(20) No(10)
• Probability of hitting target=1/4,given.Aim that the target is hit is achieved if he hits in either 1st or 2nd or 3rd or 4th shot.
  So, probability of hitting the target=P(hitting in 1st shot)+P(hitting in 2nd shot)+P(hitting in 3rd shot)+P(hitting in 4th shot)=1/4+1/4+1/4+1/4= 1 ans
• 12 years agoHelpfull: Yes(14) No(6)
• Probability of hitting the target= 1- probability of not hitting the target,
  
  if he hits once every 4 balls,
  
  probability of hitting = 1/4,
  probability of not hitting =3/4,
  
  probability of not hitting the target all four times = (3/4)* (3/4)* (3/4)* (3/4)
  
  probability of hitting target = 1 -(3/4)^4
  
  So, Finally the answer is, 1 - (81/256) = (256-81)/256 = 175/256
• 7 years agoHelpfull: Yes(9) No(0)
• 1 - P(he misses all four times)
  
  Probability of a hit in one shot =
  Probability of a miss in one shot =
  
  1 - P(misses 1st time AND misses 2nd time AND misses 3rd time AND misses 4th time)
  
  "AND" means "MULTIPLY":
  
  1 - P(misses 1st time)*P(misses 2nd time)*P(misses 3rd time)*P(misses 4th time)
  
  
  
  or about 68% of the time.
• 12 years agoHelpfull: Yes(4) No(1)
• Solution:
  
  The man will hit the target even if he hits it once or twice or thrice or all four times in the four shots that he takes.
  
  So, the only case where the man will not hit the target is when he fails to hit the target even in one of the four shots that he takes.
  
  The probability that he will not hit the target in one shot =1- Probability of he will hit target in exact one shot
  
  Therefore, the probability that he will not hit the target in all the four shots =(
  3
  4
  )×(
  3
  4
  )×(
  3
  4
  )×(
  3
  4
  )=
  81
  256
  
  
  Hence, the probability that he will hit the target at least in one of the four shots:
  =(1−
  81
  256
  )
  = 175/256
• 8 years agoHelpfull: Yes(1) No(0)