Question 1151102
.


            I edited the post at some places to make / (to create) sense where it was absent . . . 


            My editing are underlined or crossed words.



A factory has 36 male workers and 64 female workers, with 10 male workers earning less than $900 a month 
and 17 female workers earning at least $900 a month. At the end of the year, workers earning less than $900 
are given a bonus of $350, whereas the others receive a bonus of a month's salary.


<pre>
i)  <U>A worker is selected randomly</U>
    Find the probability <U>that he or she is</U> a male worker <U>receiving</U> a bonus of a month's salary or female worker receives bonus of $350.


    The probability  P = {{{(36-10)/(36+64)}}} + {{{(64-17)/(36+64)}}}.



ii) if 4 workers are chosen, find the probability that they are  {{{highlight(cross(more))}}}  workers who  {{{highlight(cross(are))}}}  earn at least $900 a month, 
    if it is known that they are female workers.


    The probability  P = {{{(C[17]^4)/(C[64]^4)}}} = {{{(17/64)*(16/63)*(15/62)*(14/61)}}}.



iii) if 3 workers are chosen at random. Find the probability that they are all female workers {{{highlight(cross(receives))}}} <U>receiving</U> a bonus of $350.


     The probability P = {{{((64-17)/100)*((64-18)/99)*((64-19)/98)}}}.



iv) if 2 workers are randomly chosen, finds the probability that only one workers receives a bonus of $350.



    In this last question, may I restrict myself, giving only HINT without detailed formula ?


        The probability is the sum of four terms  (man*man) + (man*woman) + (woman*man) + (woman*woman).


    Here the first position in parentheses is the probability for the person who receives only bonus; 
    the second position is the probability for the person from the opposite category.


    In the last formula, do not forget to include the binomial coefficients (!)
</pre>