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 :)
Once the third alternative is eliminated, you have a 50% chance of being correct, whether or not you switch. Do you want to flip a coin?
To find the experimental probabilities, we can simulate the game by using index cards. Let's use one index card marked as the prize and two other index cards unmarked as non-prize options.
A: If your strategy is to stay with your original choice, it means you do not switch the door after the host opens one of the other doors. To simulate this strategy, follow these steps:
1. Shuffle the three index cards (one prize and two non-prize).
2. Close your eyes and randomly choose one of the cards as your initial choice.
3. The host, who knows where the prize is, opens one of the remaining non-prize cards.
4. Determine if your initial choice was correct by checking if you selected the prize card.
5. Repeat this process multiple times (at least 100) and count how many times your initial choice was correct.
6. Divide the number of times you were correct by the total number of trials to get the experimental probability of winning if you stayed with your original choice.
B: If your strategy is to switch to the other door after the host opens one of the other doors, follow the same steps as above, except in step 3, switch your choice to the remaining unopened door after the host reveals a non-prize card.
C: To determine whether you should stay or switch in this game, compare the experimental probabilities from parts A and B. The strategy with the higher experimental probability would be more advantageous. The reasoning behind this is based on the concept called the Monty Hall problem, named after the host of a popular game show.
In the Monty Hall problem, it has been mathematically shown that switching doors after the host reveals a non-prize door increases your chances of winning the prize. This might be counterintuitive at first, but the key is that the host has additional information and strategically opens a non-prize door, which provides you with new information. Switching doors takes advantage of this information and increases your probability of selecting the prize.
Therefore, the experimental probability of winning if your strategy is to switch to the other door (part B) should be higher than the experimental probability of winning if you stay with your original choice (part A). Thus, you should switch in this game to maximize your chances of winning the prize.