A plane is missing and is presumed to have crashed in one of two regions: R1 or

Question

A plane is missing and is presumed to have crashed in one of two regions: R1 or R2. Field experts from NTSB have projected that there is a 30 percent chance that the plane crashed in Region 1 and there is a 70 percent chance that the plane crashed in region 2. A search party will be successful at finding the crashed plane with probability 0.8 for Region1 and 0.4 for Region 2. (a) What is the probability that the crashed plane will be found in Region 2? (b) What is the probability that the crashed plane will not be found? (c) What is the probability that the plane crashed in Region 1 given that the search was successful?

Explanation / Answer

PLEASE RATE ME FIRST Let events A = Plane crashed in region 1 A' = Plane crashed in region 2 S = Search party successful in finding plane in region 1 T = Search party successful in finding plane in region 2 a) reqd Prob = P(A')*P(T) = 0.3*0.4 = 0.12 b) reqd prob = (1-P(S))*(1-P(T)) = 0.2*0.6 = 0.12 c) reqd prob = P(A)*P(S)/(P(A)*P(S) + P(A')*P(T)) = 0.7*0.8/(0.7*0.8 + 0.3*0.4) = 0.8235

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