The probability of Jack hitting a target is 1/4. How many times must he fire so that the probability of hitting the target at least once is greater than 2/3?

Kendra Hudson 2022-09-13 Answered
The probability of Jack hitting a target is 1/4. How many times must he fire so that the probability of hitting the target at least once is greater than 2/3?
using the formula ( n C x ) ( p x ) ( ( p ) n x )
I identified p = 1 / 4, p = 3 / 4, x = ?, n = ?
in order to solve this que, I have to solve x but i couldn't identified it.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Isaiah Haynes
Answered 2022-09-14 Author has 16 answers
Step 1
Assuming Jack fires n times and X being the number of times Jack hits the target, you have that
P ( X 1 ) = 1 P ( X = 0 ) = 1 ( n 0 ) ( 1 4 ) 0 ( 3 4 ) n = 1 ( 3 4 ) n .
Step 2
Now, find n so that the expression above is greater than 2 3

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-05-21
At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in a typical cluster? With what standard deviation?
asked 2021-09-23
Compute the probability of X successes, using Table B in appendix A.
n=12,p=0.90,x=2
I believe they are using the the binomial probability formula and im not sure how to start if you can give a step by step anwser explanation that would be helpful.
asked 2021-02-19
Convert the binomial probability to a normal distribution probability using continuity correction. P (x = 45).
asked 2021-12-18
A geological study indicates that an exploratory oil well should strike oil with probability of 0.2. What is the probability that
A. the first strike comes on the third well drilled?
B. the third strike comes on the seventh well drilled?
C. What assumptions did you make to obtain the answers to parts A and B?
asked 2021-12-13
You have 165 observations of experiments in which a subject tried to guess which of 4 videos a psychic "sender" was watching in another room. Of the 165 cases, 61 resulted in successful guesses. What sort of distribution is this from? What are the sample mean and standard deviation? Compute a 95% confidence interval for the probability of a successful guess. Does this convince you of ESP? Why or why not?
asked 2022-09-17
Comparing Binomial Probability to Poisson Random Variable Probability
A text file contains 6000 characters. When the file is sent by e-mail from one machine to another, each character (independently of all other characters) has probability 0.001 of being corrupted. Use a Poisson random variable to estimate the probability that the file is transferred without error.
Compare this to the answer obtained when you model the number of errors as a binomial random variable.
For the binomial probability I got 0.2471%(to 4 significant figs).
For the Poisson probability I got 0.2478%(to 4 significant figs).
However I'm not sure how I'm supposed to compare them, clearly I can see that the binomial probability is slightly lower, but I don't understand why this is the case?
asked 2021-09-17
X denotes a binomial random variable with parameters n and p, Indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability.
P(X8)

New questions

Question on designing a state observer for discrete time system
I came through this problem while studying for an exam in control systems:
Consider the following discrete time system
x ( k + 1 ) = A x ( k ) + b u ( k ) , y ( k ) = c x ( k )
where b = ( 0 , 1 ) T , c = ( 1 , 0 ) , A = [ 2 1 0 g ] for some g R
Find a feedback regulation (if there is any) of the form u ( k ) = K x ^ ( k ) where x ^ ( k ) is the country estimation vector that is produced via a linear complete-order state observer such that the nation of the system and the estimation blunders e ( k ) = x ( k ) x ^ ( k ) go to zero after a few finite time. layout the kingdom observer and the block diagram.
My method
it is clean that the eigenvalues of the machine are λ 1 = 2 , λ 2 = g (consequently it is not BIBO solid) and that the pair (A,b) is controllable for every fee of g, as nicely a the pair (A,c) is observable for all values of g. consequently we will shift the eigenvalues with the aid of deciding on a benefit matrix okay such that our device is strong, i.e. it has its eigenvalues inside the unit circle | z | = 1.
The state observer equation is
[ x ( k + 1 ) e ( k + 1 ) ] T = [ A b K B k O A L C ] [ x ( k ) e ( k ) ] T
With characteristic equation
χ ( z ) = | z I A + b K | | z I A + L C | = χ K ( z ) χ L ( z )
Also consider
K = [ k 1 k 2 k 3 k 4 ]
and let a = k 1 + k 3 , β = k 2 + k 4
Then χ K ( z ) = ( z 2 ) ( z + g + β ) + a.
So we can select some eigenvalues inside the unit circle and determine a , β in terms of g. Choosing e.g. λ 1 , 2 = ± 1 / 2 we get a = 3 g + 33 / 8 , β = 9 / 4 g , g R
Questions
I want to ask the following:
Is my approach correct? Should I select the eigenvalues myself since I am asked to design the observer or should I just solve the characteristic equation and impose | λ 1 , 2 | < 1?
Should I determine L matrix as well since the error must also vanish? (because it is not asked)