Patrick inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back. Patrick doesn't know it, but in the batch he is inspecting now, there are 100 products and 12 are defective. If he samples 4 products from this batch without replacement,what is the probability that...     a) All of the products in the sample will be defective?              b) None of the products in the sample are defective?              c) At least one of the products is defective and the whole batch is sent back?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Patrick inspects a batch of products by sampling 4 of them without replacement. If at least one of the products is defective in the sample, the whole batch is sent back.

Patrick doesn't know it, but in the batch he is inspecting now, there are 100 products and 12 are defective. If he samples 4 products from this batch without replacement,what is the probability that...


    a) All of the products in the sample will be defective?
       

     b) None of the products in the sample are defective?
       

     c) At least one of the products is defective and the whole batch is sent back?
       

For all of the above, round to four decimal places.

(answer a b c)

Expert Solution
Step 1

Sol:-

a) The probability of selecting all 4 defective products without replacement is:

(12/100) * (11/99) * (10/98) * (9/97) = 0.00000351

Therefore, the probability that all of the products in the sample will be defective is approximately 0.0000.

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman