A study of major flash floods that have occured in the last 20 years shows that the probability that a flash flood warning is issued (W) is 0.10. The probability of a dam failure (D) during the flood is 0.38. If a flash flood warning is issued, the probability of a dam failure (D) during the flood is 0.17. Find the probability that a) a flash flood warning is issued and there is a dam failure, b) a flash warning is issued or there is a dam failure, c) a flash flood warning is issued given that there is a dam failure, d) are the events W and D independent? e) are the events W and D mutually exclusive?