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?

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Mathematics

Danny Downs

27 January, 18:39

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?

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Dreamer · Answer 1

The probability is 75.7%.

70% of women are married. Of these, 20% own a dog; this means that P (dog and married) = 0.7 (0.2) = 0.14.

Since 70% are married, 100-70=30% are single. Of these, 15% own a dog; this means that P (dog and single) = 0.3 (0.15) = 0.045.

This gives a total for dog owners of 0.14+0.045 = 0.185.

P (married given dog owner), or P (M|D), is P (dog owner and married) / P (dog owner):

P (D and M) / P (D) = 0.14/0.185 = 0.757 = 75.7%