on a tv game show,you try to win a prize that is hidden behind one of the three doors.after you choose a door, but before it is open,the host opens one of the other doors,behind which there is no prize.you can then switch the remaining closed door or stay with your orginial prize.
A: find the experimental probability of winning if your stragety is to stay with your orginal choice( hint:simulate by using one marked index card and two unmarked index cards.
B: find the experimental probability of winning if your stragety is to switch to the other door.
C: should you stay or switch in this game. Explain??
please help me i am confused...
thank you :)
i still don't get it
I can help you understand the game show and determine the best strategy. Let's break down the problem step by step.
The game show scenario involves three doors, behind one of which is a prize. Your goal is to choose the door that hides the prize. The host knows which door has the prize.
After you make your initial choice, the host, who knows where the prize is located, opens one of the other doors that does not have the prize behind it. This step is crucial to understanding the optimal strategy.
Now, let's address your questions:
A: To find the experimental probability of winning if you choose to stay with your original choice, you can simulate the game using three index cards. Mark one card as the prize and leave the other two unmarked. Shuffle the cards and randomly select one as your original choice. Then, look at the result and determine if you won. Repeat this process a large number of times, like 100 or 1000, and calculate the proportion of times you won. This proportion will give you an estimate of the experimental probability of winning if you choose to stay.
B: To find the experimental probability of winning if you choose to switch to the other door, you can simulate the game using the same procedure as in question A. But this time, after the host opens one door without the prize, switch your choice to the remaining unopened door. Again, repeat the simulation many times and calculate the proportion of times you win. This proportion will give you an estimate of the experimental probability of winning if you choose to switch.
C: To determine whether you should stay or switch, compare the experimental probabilities of winning from questions A and B. The strategy with the higher experimental probability of winning is the better strategy. If the experimental probability of winning is higher when you choose to switch, then switching is the better strategy.
The answer to this question is a bit counterintuitive. If you simulate the game and calculate the experimental probabilities, you will find that the strategy of switching to the other door gives you a higher probability of winning compared to the strategy of staying with your original choice. This result is known as the Monty Hall problem, and it has been mathematically proven that switching is the optimal strategy.
I hope this explanation helps you understand the game show scenario and how to determine the best strategy.