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Math Help - probability and stastistics

  1. #1
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    probability and stastistics

    the probability that an automobile filled with gasoline will also need an oil change is 25%.the probability that it needs a new filter is 40% and the probabilty that both the oil and filter need changing is 14%
    a.)If the oil had to be change.What is the probabilty that a new oil filter is changed?
    b.)If the new filter to be change.What is the probability that the new oil is changed?
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  2. #2
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    Hello, alderon!

    Use Bayes' Theorem: . P(A \,|\,B) \;=\;\frac{P(A \cap B)}{P(B)}


    The probability that a car will need an oil change is 25%.
    The probability that it needs a new filter is 40%.
    The probabilty that both the oil and filter need changing is 14%.

    a) If the oil had to be changed, what is the probabilty that a new filter is needed?
    b) If the filter had to be changed, what is the probability that the oil is changed?
    We are given: . \begin{array}{ccc}P(\text{oil}) & = & 0.25 \\ P(\text{filter}) & = & 0.40 \\ P(\text{oil}\cap\text{filter}) & = & 0.14\end{array}


    a)\;P(\text{filter}\cap\text{oil}) \;=\;\frac{P(\text{filter}\cap\text{oil})}{P(\text  {oil})} \;=\;\frac{0.14}{0.25} \;=\;0.56

    b)\;P(\text{oil}\cap\text{filter}) \;=\;\frac{P(\text{oil}\cap\text{filter})}{P(\text  {filter})} \;=\;\frac{0.14}{0.40} \;=\;0.35

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  3. #3
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    Smile thanks!!!

    thanks...buddy...
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