SOLUTION: Suppose that in a population of women 70% are married, 20% of the married women own a dog and 15% of the single women own a dog. If a randomly selected woman owns a dog, what is th

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Question 1115530: Suppose that in a population of women 70% are married, 20% of the married women own a dog and 15% of the single women own a dog. If a randomly selected woman owns a dog, what is the probability she is married?
Answer by ikleyn(52908) About Me  (Show Source):
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According to the condition


    Of a population of every 1000 women 700 are married. 

        Of them, 20%, i.e.  %28700%2A%2820%2F100%29%29 = 140 own a dog.



    Of the same population of 1000 women 300 are single,

       and of them, 15%, i.e.  300%2A%2815%2F100%29 = 45  own a dog.



Now we are ready to answer the question, and the answer is  140%2F%28140%2B45%29 = 140%2F185 = 28%2F37 = 0.7568 = 75.68%.