Question

Bill and Joe decided to go on vacation together. Bill lives in Boston, and Joe lives in New York. They flip a coin to decide if they will fly from Boston or from New York, and then they flip a coin again to decide if they will go to Miami or to Las Vegas. Flight time between Boston and New York is 1 hour, and flight times from either of these cities to Miami and Las Vegas are 3 hours and 5 hours respectively. Find the mathematical expectation of the total flight time for Bill from his home city to their vacation destination.

Answer 1

Expected value for the first flight:

	Fly from Boston	Fly from New York
P	0.5	0.5
x	0	1

E(x) = 0.5*0 + 0.5*1 = 0.5 hours

Expected value for the second flight:

	Fly to Miami	Fly to Las Vegas
P	0.5	0.5
x (Time)	3	5

E(x) = 0.5*3 + 0.5*5 = 1.5 + 2.5 = 4 hours.

Hence, total expected flight time for Bill = 0.5 + 4 = 4.5 hours.

Please comment if any doubt. Thank you.