Puzzle 20

Hi!

I'm creating an archive for my puzzles, so you can see all the past puzzles! Hope you don't mind the extra sidebar content...

Anyway if it gets too long I'll try to minimize it.

Here's (the late) Puzzle 20!

LUCK AND PROBABILITY (PART 2)

Difficulty: Easy

Okay... I'll give you people a break since the previous puzzle was a "Very Hard" puzzle.

You are faced with 3 doors. One of them leads to the escape while the other 2 lead to a dead end. You are only allowed to open 1 door.

Suppose you pick one of the 3 doors. A door (which you didn't pick) that leads to a dead end is automatically opened for you. You are then allowed to switch your choice, to the other unopened door.

Should you change your mind? By how much does your chance of opening the wrong door change if you decided to switch doors?


Now for the answer to Puzzle 19...

1) It's surprisingly, 2/3, not 1/2!

There are only 3 faces which have circles on them: 2 of which are on the same card, while the last face with a circle has a cross marked on the other face. So, when you place the card face-up on the table, there's a 2/3 chance that the face facing you is one of the 2 faces with a circle that are on the same card. Hence, the answer is 2/3.

This is also known as the three-card swindle or the card version of Bertrand's box Paradox.

2) You'll most likely end up losing money :(

There's only 1/4 chance of you getting tails 2 times (NOT 1/3!). Hence, on average, for every $1.50 you give your friend, you get only $1.20 of it back.

No Joyce, you can't use any of these tricks to con people!

:)
Glen