Question 1183648
.
The quality assurance engineer of a receiving-sets manufacturer inspects receiving-sets in lots of 50. 
He selects 4 of the 50 receiving-sets at random and inspects them thoroughly. 
Assuming that 5 of the 50 receiving-sets in the current lot are defective, find the probability 
that exactly 3 of the 4 receiving-sets selected by the engineer are defective.
~~~~~~~~~~~~~~~~~~~~~~


<pre>
P = {{{(C[5]^3*C[50-5]^1)/C[50]^4}}} = {{{(C[5]^3*C[45]^1)/C[50]^4}}} = {{{(10*45)/230300}}} = {{{9/4606}}} = 0.001954.      <U>ANSWER</U>



The numerator of P,  {{{C[5]^3*C[45]^1}}},  is the number of favorable combinations of 4 of the 50 receiving-sets, 
that contain exactly 3 defective receiving-sets and one good receiving-set.


It is the favorable set.


The denominator is the total number of 4 receiving-sets selected by the engineer from 50 receiving-sets.


The probability, as always in such problem, is the ratio  {{{favorable/total}}}.
</pre>

Solved.


-----------------


To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-combinations-REVISITED.lesson>Elementary Probability problems related to combinations REVISITED</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.


Consider these lessons as your textbook,  &nbsp;handbook,  &nbsp;a Solutions Manual, &nbsp;tutorials and &nbsp;(free of charge)  &nbsp;home teacher.



Happy learning (!)