HallsofIvy said:The question is "does 'after'" mean "immediately after" or would five hits and then a miss be "the first miss is after the first three shots".
If you mean the first, then, yes, (.9)^3(.01) is correct.
If the second, then you need to expand that to larger numbers of initial hits:
(.9)^3(.01)+ (.9)^4(.01)+ (.9)^5(.01)+...
You might recognize that as part of a geometric sequence and so find a simple formula for sum.
The probability of a sharpshooter missing after 3 shots depends on various factors such as the skill level of the sharpshooter, the distance of the target, and the type of weapon used. Generally, if we assume that the sharpshooter has a high level of accuracy, the probability of missing after 3 shots would be very low, close to zero.
The distance of the target plays a significant role in the probability of a sharpshooter missing after 3 shots. The further the target is, the higher the chances of missing as it becomes more challenging to maintain accuracy at longer distances. However, skilled sharpshooters may still have a low probability of missing even at longer distances.
Yes, the type of weapon used can affect the probability of a sharpshooter missing after 3 shots. Different weapons have different levels of accuracy and recoil, which can impact the sharpshooter's ability to maintain accuracy after multiple shots. A weapon with high accuracy and low recoil would result in a lower probability of missing after 3 shots.
Yes, the probability of a sharpshooter missing after 3 shots can be calculated using mathematical equations and statistical analysis. However, the accuracy of the calculation depends on the accuracy of the data used and the assumptions made in the calculation.
Apart from the skill level, distance, and weapon used, other factors that can affect the probability of a sharpshooter missing after 3 shots include environmental conditions such as wind, lighting, and terrain. These factors can impact the trajectory of the bullet and ultimately affect the sharpshooter's accuracy.