SOLUTION: 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

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Question 1151102: 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.
i)Find the probability that a male worker receives a bonus of a month's salary or female worker receives bonus of $350.
ii) if 4 workers are chosen, find the probability that they are more workers who are earn at least $900 a month if it is known that they are female workers.
iii) if 3 workers are chosen at random. Find the probability that they are all female workers receives a bonus of $350.
iv) if 2 workers are randomly chosen, finds the probability that only one workers receives a bonus of $350.
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Answer by ikleyn(52855) About Me  (Show Source):
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            I edited the post at some places to make / (to create) sense where it was absent . . .

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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. 

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


    The probability  P = %2836-10%29%2F%2836%2B64%29 + %2864-17%29%2F%2836%2B64%29.



ii) if 4 workers are chosen, find the probability that they are  highlight%28cross%28more%29%29  workers who  highlight%28cross%28are%29%29  earn at least $900 a month, 
    if it is known that they are female workers.


    The probability  P = %28C%5B17%5D%5E4%29%2F%28C%5B64%5D%5E4%29 = %2817%2F64%29%2A%2816%2F63%29%2A%2815%2F62%29%2A%2814%2F61%29.



iii) if 3 workers are chosen at random. Find the probability that they are all female workers highlight%28cross%28receives%29%29 receiving a bonus of $350.


     The probability P = %28%2864-17%29%2F100%29%2A%28%2864-18%29%2F99%29%2A%28%2864-19%29%2F98%29.



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 (!)