The Monty Hall problem is a game with a number of choices we will call Total, so

Question

The Monty Hall problem is a game with a number of choices we will call Total, some of which are Good and some Bad. Good must be 2 1 and Bad 2 2. In the game, you bad choice is revealed. You are asked then whether you want to stay on your original choice or switch to another. The probability of success in each case is as follows. Write the answers below as decimal numbers rounded to the nearest thousandth. (4 points) make an initial choice, then onde Stay: Total Switch: Good × Total-1 Total Total-2 p (Stay): p(Switch): Total = 5, Good = 1, Bad = 4 p(Switch): p(Stay): Total = 5, Good = 2, Bad = 3

Explanation / Answer

Total = 5 , good = 1 , bad = 4

p(stay) = good / total = 1/5 = 0.200

p(switch) = good / total * total -1 / total -2 = 1/5* 5-1/5-2 = 1/5 * 4/3 = 4/15 = 0.267

Total = 5 , good = 2 , bad = 3

p(stay) = good / total = 2/5 = 0.400

p(switch) = good / total * total -1 / total -2 = 2/5* 5-1/5-2 = 2/5 * 4/3 = 8/15 = 0.533

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