Question 1164818
.
A lot of 75 washers contains 5 in which the variability in thickness around the circumference
of the washer is unacceptable. A sample of 10 washers is selected at random, without
replacement.
(a) What is the probability that none of the unacceptable washers is in the sample?
(b) What is the probability that at least one unacceptable washer is in the sample?
(c) What is the probability that exactly one unacceptable washer is in the sample?
(d) What is the mean number of unacceptable washers in the sample?
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<pre>
(a)  What is the probability that none of the unacceptable washers is in the sample?


     One way to calculate is to use the formula

         P = {{{C(75-5,10)/C(75,10)}}} = {{{C(70,10)/C(75,10)}}} .


     The numerator   is the number of favorable    choices from 70 good washers taken 5 at a time;
     the denominator is the number of all possible choices from 75 washers taken 5 at a time.


     This is the ratio of two very big numbers (12-digits or 11-digits).


     They can be calculated in the scientific format, but this way does not give the feeling of numbers.
     So, I prefer another (equivalent) formula

         P = {{{(70/75)*(69/74)*(68/73)*(67/72)*(66/71)*(65/70)*(64/69)*(63/68)*(62/67)*(61/66)}}} = 0.4786  (rounded).   <U>ANSWER</U>

     This formula is self-explanatory.


     Part (a) is solved.



(b)  What is the probability that at least one unacceptable washer is in the sample?


     This probability is the complement

         P' = 1 - P = 1 - 0.4786 = 0.5214  (rounded).    <U>ANSWER</U>


     Part (b) is solved.



(c)  What is the probability that exactly one unacceptable washer is in the sample?


     One way to calculate is to use the formula

         P = {{{C(10,1)*C(74,9)/C(75,10)}}}.


     Again, this is the ratio of two very big numbers (12-digits or 11-digits).


     They can be calculated in the scientific format, but this way does not give the feeling of numbers.
     So, I prefer another (equivalent) formula

     P = {{{(70/75)*(69/74)*(68/73)*(67/72)*(66/71)*(65/70)*(64/69)*(63/68)*(62/67)}}} = 0.5178  (rounded).   <U>ANSWER</U>


     Part (c) is solved.



(d)  What is the mean number of unacceptable washers in the sample?

     
     It is  {{{5/75}}} = {{{1/15}}}.
</pre>

Solved.  All questions are answered.



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I submit this my solution as an opposition to the post by @CPhill.


I want you see the difference between a true Math solution, 
which teaches on how to solve a typical Math problem by a traditional way and how to makes it effectively
in opposite to the post by @CPhill, which is the run of the undebugged computer code
and demonstrates how the Artificial Intelligence should not communicate with a user.