SOLUTION: Every morning you roll a die to decide how much to run. If you get a 1, you will run 2 miles. If you get a 2, 3 , or a 4, you will run 3 miles. Finally, if you get a 5 or 6, you ru

Question 1083838: Every morning you roll a die to decide how much to run. If you get a 1, you will run 2 miles. If you get a 2, 3 , or a 4, you will run 3 miles. Finally, if you get a 5 or 6, you run 4 miles. In the long run, how much will you be running on average per day? In other words, if you keep a record of how much you are running every dayand after a long time take an average, then what will this average be approximately?
Hint: start with assuming that you are going to run for 300 days. How many dies would you run 2 miles, three miles, or four miles? What's the average? What if you run for 600 days? When you do that, answer the original question.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
(1/6) probability will get a 1 and run 2 miles, 50 days out of 300, 100 days out of 600.
(1/2) probability get 2,3,4 and run 3 miles, 150 days out of 300, 300 days out of 600.
(1/3) probability get a 5,6 and run 4 miles, 100 days out of 300, 200 days out of 600.
In 300 days would run 100+450+400=950 miles or 3.17 miles a day.
In 600 days would run 200+900+800=1900 miles or 3.17 miles a day.
That is the expected value
(1/6)(2)+(1/2)*3+(1/3)*4=(1/3)+(3/2)+(4/3)=(38/12)=3.17 (3 1/6)
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