Hi! Doubt in probability question from the bag of pratice questions on the website.
Here, to find 2/3 we are only considering the case where Divya picks the first ball.
Should we not apply permutations here, and consider similar cases where Divya picks ball # 2 and ball # 3? Adding all these up, the final probability will be 6/9.
Please do help me with where my logic is going wrong here, thanks
If we assume, without loss of generality, that the ball is under Cup #1, we then have three possible cases based on Divya’s initial choice:
Divya picks Cup #1 → She loses after a switch
Divya picks Cup #2 → She wins after a switch
Divya picks Cup #3 → She wins after a switch
You can certainly “recycle” this entire process, first assuming the ball is now under Cup #2, and then again assuming it’s under Cup #3. What you come to realize is that this problem is isomorphic (symmetric) in nature. Owing to that, it is sufficient to analyze just one of these initial setups (e.g., the ball being under Cup #1) to compute the require probability.
Ahh! Understood- thank you so much!
