2. (30 points) You invest money in two hotels (A and B) located close to each other on the lake but in a potential flood zone. During a flood, the probability of damage to Hotel A is o.15 and the probability of damage to Hotel B is o.2. It is also known that if Hotel B is damaged, there is a 40% chance that Hotel A will be damaged as well. (i). In a flood, what is the probability that at least one hotel damaged? (5 points) Now consider Eo, E, and Ez defined such that: E.: Event { no hotel is damaged} Ex: Event { Exactly ONE hotel is damaged} Ex: Event { Both hotels are damaged} (ii). Determine P(E.), P(E.), and P(E,). (15 points) To plan ahead, decide to purchase insurance against property damage during floods. With such insurance, you are told that there will be a 10% chance of serious financial losses if only one of hotels were damaged but a 25% chance if both hotels are damaged. Assume that no losses result if neither hotel is damaged. (iii). What is the probability that you will incur serious financial losses? (5 points) (iv). Assume now that floods have occurred and serious financial losses result. What is the probability that both of the hotels suffered damage? (5 points) P(A) = 0.15 P(B)= 0.2 P(AlB ) = 0.4 (1) let PLA, = hotel A got no damage : 1- U.15 0.85 P(B) = hotel B gol no damage : 1 - 0.2 = 0.8 at least I hotel olawaged : 1 - no damage at all : 1 - 0.85 . 08 0. 32 ( 11) P( EO) : 0185 x 0.8 : 10.68 P ( EI ) : 0.32 - 0: 03: 10 29 P (E . ) : 0. 15 x 0. 2 = 10.03 ( 11 1 ) 0. 29 x 0. 1 + 0-03 x 0, 25 : 01 0365 + 3 Probability incur serious financial losses : P(2 ) = 0-0361 ( iv ) P ( E 2 12 ) = ( E, ML ) PEZ ) + 3