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2.3 Exercise 13

Avg difficulty 2.5

During a period of unsettled weather, let A be the event of rain in Austin, B be the event of rain in Houston, and C be the event of rain in San Antonio. Suppose:

P ( A B ) = 0 . 35 , P ( A B c ) = 0 . 15 , P ( A C ) = 0 . 20 , P ( A B c ∪ A c B ) = 0 . 45 P \left(A B\right) = 0 . 35 , P \left(A B^{c}\right) = 0 . 15 , P \left(A C\right) = 0 . 20 , P \left(A B^{c} \cup A^{c} B\right) = 0 . 45
P ( B C ) = 0 . 30 P ( B c C ) = 0 . 05 P ( A c B c C c ) = 0 . 15 P \left(B C\right) = 0 . 30 P \left(B^{c} C\right) = 0 . 05 P \left(A^{c} B^{c} C^{c}\right) = 0 . 15
  1. What is the probability of rain in all three cities?
  2. What is the probability of rain in exactly two of the three cities?
  3. What is the probability of rain in exactly one of the cities?

Pfeiffer, Applied Probability, 2.3 Problems on Minterm Analysis, exercise 13

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Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.