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Math Help - Probability help

  1. #1
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    Probability help

    A Resturant owner knows that female employees are more reliable at work then male employees, so he employs 70% Female employees and 30% Males at his restaurant. He also knows that out of the female employees 4% cannot complete their work satisfactorily and out of the males 2% cannot complete their work satisfactorily.

    1.) What is the probability that he will find an employee who does not compelete their work satisfactorily on any given day?

    2.) One day he found that an employee has done unsatisfactory work. what is the probability that the work was done by a male employee

    I'm stumped and suck at these probability problems
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  2. #2
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    Re: Probability help

    Quote Originally Posted by polaris10108 View Post
    A Resturant owner knows that female employees are more reliable at work then male employees, so he employs 70% Female employees and 30% Males at his restaurant. He also knows that out of the female employees 4% cannot complete their work satisfactorily and out of the males 2% cannot complete their work satisfactorily.
    1.) What is the probability that he will find an employee who does not compelete their work satisfactorily on any given day?
    \begin{align*}\mathcal{P}(U) &=\mathcal{P}(U\cap M)+\mathcal{P}(U\cap F)\\&=\mathcal{P}(U|M)\mathcal{P}(M)+\mathcal{P}(U  |F)\mathcal{P}(F)\end{align*}.
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  3. #3
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    Re: Probability help

    1) .7x.04+.3x.02=...
    2) I forget
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  4. #4
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    Re: Probability help

    Quote Originally Posted by polaris10108 View Post
    A Resturant owner knows that female employees are more reliable at work then male employees, so he employs 70% Female employees and 30% Males at his restaurant. He also knows that out of the female employees 4% cannot complete their work satisfactorily and out of the males 2% cannot complete their work satisfactorily.
    2.) One day he found that an employee has done unsatisfactory work. what is the probability that the work was done by a male employee
    \mathcal{P}(M|U)=\frac{\mathcal{P}(U|M) \mathcal{P}(M)}{\mathcal{P}(U|M) \mathcal{P}(M)+ \mathcal{P}(U|F)\mathcal{P}(F)}
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