"You are on a game show where the host asks you to select one of three doors. Behind one door is a prize, but both of the other doors have nothing. You cannot tell which door has the prize so you must guess the correct door to win. After selecting door #2, the host reveals the contents of door #3 to be empty, so the prize is still available. The host then asks, “Before we reveal the contents of the next door, do you want to switch your answer?”. You decide to change your guess to door #1. Multiply the probability you win the prize by 200, then round the answer to the nearest whole number."
We did this at school, but all I remember is that your likelihood of winning is better if you change...
It's this:
en.wikipedia.org
"Vos Savant's response was that the contestant should switch to the other door.
[3] Under the standard assumptions, the switching strategy has a 2/3
probability of winning the car, while the strategy that remains with the initial choice has only a 1/3probability."
So 2/3 is the probability we need to multiply I think