If there are two boxes. The first has a 100$ bill and a 1$ bill, and the second has two 100$ bills. If I puck a random box and take out a 100$ bill, whaat is the chance of me taking out another 100$ bill?

Question

I’m honestly stuck. I’ve seen people say 1/2, others 2/3. Something Monty Hall Problem, Bayes Theorem but I’m still confused so here I am.

Edit: I believe you are not allowed to change your box choice on the 2nd “turn” as that would make having two boxes pointless, wouldn’t it?

In: 10

Answer 1

It’s 2/3. There’s plenty of explanations already in the topic, so I coded up a small simulation to test your scenario. You can run the linked code by clicking on the triangle button at the top.

[First simulation.](https://tio.run/##lZPBbqMwEIbPyVPMRpUWSkuTXtleVt3DHiqtlGOUgwMmcQI2soeGKOLZs@MBGlp1pW0kwjCe/xvPj9mLV3G/zw6XiyorYxH2lIgLobfxbTKdVvWmUCmkhXAOXoTScJ5O@qRDgXR7NSqD0i8FS7RKb1drEHbrQsCdNUc3Iv5qUlmhMkyZKI2QWXFcwBPMk3FiPh9SubEQ@LziDN1@AC3Tj@IoChnkhas1td2YRjoqPJ@p5s4XtnfQx22bwMMDLCXWFRXirqvu5ZAr6/CnaUjt@4UQvAjcxVbozJRBCLfwGDLgj0oPNJn041ukcT3nPUUVBWEYvxq469U/sWvmPtPgnR42HpBbU37eJ4fg2ufbkx@z92GSGk2ltWTi75z1HdP7Csrp7wg3bEhmfMxwLpNNJa0qpcZhLTW1N/7tmdbpdZSccQdVARpWatkQwp78Dlr/521m7pUJR0WOd1vx/UEUVorsxPvSg31O0gDZO/8WcA9f87CDfDCR3re0YwfHrcjCwUA@flGUvM3ySe3V7v6wjur9tTw5lGVsaowr@h6w0MHs2cojzCDqD3xE8c2C9@jiWZj8l4pc63QUjJTttL1c/gI) This is the scenario if you draw the first bill from one box, and the second bill from the other box. The result I’m getting is:

> Drew 24991 $1 bills.
> Drew 50331 $100 bills.

[Second simulation.](https://tio.run/##jVPBbqMwED0nXzEbVVooLU16ZXupuoceKq2UY5SDA07iBGxkDw1RxLdnZwwhVN1qiwQMM@89D2/snXgX97tsfz6rojQWYUeJOBd6E98m43FZrXKVQpoL5@BNKA2n8ahLOhRIr3ejMii4FMzRKr1ZLEHYjQsBt9Yc3EDxd53KEpXxKiOlETIrDjN4gmkyTEynl9TaWAg4r3yGXr@AynRRHEWhF2LiYknLrkwtHQFPJ8LcMbC5gy5umgQeHmAusSoJiNsW3dMh3Ron9bOpScCXFrxwCMGbwG1shc5MEYRwC4/h0kv9UekeBGM7EVgr6/BZ5fmrziTrfKmQwCcOwfsWFh@V2vVeyJoWDivGr60pyGPZ0fpG1hBcRX88sQ2dT6PUaFS6kl7vde3ZrSL7Dsrpnwg33rDMcEwzpj3BMFmX0qpCarzUUlPxYPpvqtO4Cp9xe1UCGs/UsiYJe@QOGn7wGLzuVRMOiibStsLrg8itFNnR96UvXjlJP5B9MmsG9/ClYS3nv44Npcmyi2F@O0ZR0vf@D@zV3m7zDvB8z48OZRGbCuOSzgfmOpi8WHmACUTdAYgovpn5Jl08CZNvscillkfBgNmMm/P5Lw) This is the scenario is you draw both bills from the same box. The result I’m getting is:

> Drew 25056 $1 bills.
> Drew 50022 $100 bills.

Of course there’s randomness involved so the results vary a bit, but they’re always around this 25000 and 50000. So in both scenarios you have a 2/3 chance to draw a second $100 bill after having already drawn one in the first place.