Choose Wisely: The Tricky Box Puzzle #shorts #challenges #smart #funny #puzzle #math #mathematician
8You have three boxes labeled: A, B, and C. One of the boxes contains a prize, while the other two are empty. You are allowed to choose one box, but before you open it, the host, who knows which box contains the prize, opens one of the other boxes to reveal that it is empty. The host then gives you the option to switch your choice to the remaining unopened box or stick with your original choice. Which box should you choose to maximize your chances of winning the prize, and why?
The optimal strategy is to switch your choice to the remaining unopened box. This may seem counterintuitive, but it actually doubles your chances of winning the prize from 1/3 to 2/3. Here's why:
When you first choose one of the boxes, you have a 1/3 chance of choosing the box with the prize and a 2/3 chance of choosing an empty box. After the host opens one of the other boxes to reveal it is empty, there are only two boxes left: the one you chose and the remaining unopened box. If you stick with your original choice, your chances of winning remain at 1/3. However, if you switch to the remaining unopened box, you win the prize if and only if you initially chose an empty box, which occurs with probability 2/3. Therefore, by switching, your chances of winning increase to 2/3.
So, to maximize your chances of winning, you should always switch your choice after the host opens one of the other boxes to reveal an empty box.