Question

An expert sharpshooter misses a target 5 percent
of the time. Find the probability that she will
miss the target for the second time on the
fifteenth shot

Answer 1

make me think first thing in the morning
your first job is to figure out the probability that she makes exactly 13 out of her first 14 shots.
we can multiply that answer by .05 to get your answer.
is it clear why?

Answer 2

or more to the point, do you know how to figure out the first answer using the binomial distribution?

Answer 3

or would you just like me to write an answer?

Answer 4

hi explanation and answer im not ready to attempt it...have something else doing

Answer 5

hi

Answer 6

first off if i understand the question correctly, she must make exactly 13 out of the first 14 shots, and miss the 15th one right?

Answer 7

probability she misses a shot is .05 and so the probability she makes a shot must be .95
we are assuming that the shots are independent, so these are "bernoullii trials" i.e. there are only two outcomes "success" or "failure" and events are independent
therefore the probability that she makes exactly 13 out of 14 shots is
\[P(k=13)=\dbinom{14}{13}(.95)^{13}\times (.05)^1\]

Answer 8

that is 13 successes, one failure and \(\dbinom{14}{13}=14\) what to arrange the 1 failure and 14 successes

Answer 9

take this number and multiply it by \(.05\) which is the probability she misses the 15th shot
that will give you the probability she misses the her second shot on the 15th try

Answer 10

a final answer is \(14\times (.95)^{13}\times (.05)^2\) and a final final answer requires a calculator