A new surgical procedure is successful with a probability

Chapter 3, Problem 44E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

A new surgical procedure is successful with a probability of \(p\). Assume that the operation is performed five times and the results are independent of one another. What is the probability that

a all five operations are successful if \(p = .8\)?

b exactly four are successful if \(p = .6\)?

c less than two are successful if \(p = .3\)?

Questions & Answers


(2 Reviews)

QUESTION:

A new surgical procedure is successful with a probability of \(p\). Assume that the operation is performed five times and the results are independent of one another. What is the probability that

a all five operations are successful if \(p = .8\)?

b exactly four are successful if \(p = .6\)?

c less than two are successful if \(p = .3\)?

ANSWER:

Step 1 of 3

a) We have to find the probability of all operations are successful if \(p=0.8\)

And \(\begin{aligned} \mathrm{q} & =1-0.8 \\ & =0.2 \end{aligned}\)

Given that the operation is performed 5 times

Then \(n=5\)

Let \(X\) be the no.of successful operations

Then \(X \sim B(5,0.8)\)

The pmf of binomial distribution is \(P(x)=n_{C_{x}} p^{x} q^{n-x} ; x=0,1,2,3, \ldots\)

\(\begin{aligned} \mathrm{P}(\text { all operations are successful }) & =\mathrm{P}(\mathrm{X}=5) \\ & =5_{C_{5}}(0.8)^{5}(0.2)^{0} \\ & =0.32768 \end{aligned}\)

Hence the probability of all operations are successful is \(0.32768\)

Add to cart

Reviews

Review this written solution for 31495) viewed: 4429 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 3 - Problem 44e

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

Textbook: Mathematical Statistics with Applications

Click to rate

Write a review below (optional):

Submit Review
×

Thanks for your review!

Think of all the students you've helped. Nice job!

Review this written solution for 31495) viewed: 4429 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 3 - Problem 44e

Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.

Textbook: Mathematical Statistics with Applications

Click to rate

Write a review below (optional):

Submit Review
×

Thanks for your review!

Think of all the students you've helped. Nice job!


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back