A PROBABILITY PUZZLE FOR THE NEW YEAR

A friend lays out three envelopes on a table: a red one, a blue one and a green one.   He tells you that two of the envelopes have a nude picture of Donald Trump and the third has one-hundred-dollar in cash.  

The friend knows which envelope contains the one-hundred-dollars.

He tells you to pick an envelope and if you pick the one with the $100, you can keep it.

You pick the red.

Your friend tells you he will narrow the odds and opens the blue envelope and shows you Donald Trump’s ass. 

You still have the red envelope and the green remains on the table.

He asks you if you want to swap the red envelope for the green.

Should you swap?

The answer is below

Yes, you should swap.   When you picked the red envelope there was a thirty-three percent chance (33%) that you picked the envelope with cash, and a sixty-six (66%) percent chance that the envelope with the cash still remains on the table.  

Once your friend opens the blue envelope and shows Donald Trump’s ass, the probability has not changed: there is still a thirty-three percent chance that you have the cash envelope and a sixty-six percent chance that the cash envelope remains on the table – in the green envelope.  

You can test this probability results with three playing cards: two black and one red.     If you run the test forty times you will find that swapping the card is best option.