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?

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%