## Stare at the dot

This is a lovely and somewhat strange illusion. Stare at the red dot in the left-hand image for about 20 seconds, and then look at the centre of the right-hand image. All being well, lots of strange stuff will happen in your brain…..

Tagged , ,

## Probability Games (Do you suffer from probability illusions?)

I) I have just tossed a fair coin 7 times. Guess which of the four sequences below is genuine (order them according to their plausibility):

.

1) HHHHTTT

2)THHTHTT

3)HHHHHHH

4)TTTTTTH

.

.

II) A die has been painted in such way so that it has four green faces and two red. I have thrown the die repeatedly into a table and produced one of the four sequences. Which one is the genuine one (please order them according to their plausibility)?

1.RGRRR

2.GRGRRR

3.GRRRRR

.

.

Tagged , ,

## The Monty Hall problem

Consider the following problem
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

.

(Formulation by Marilyn vos Savant at Whitaker, Craig F. (1990).)
.
So what is the answer? Let’s see a simple solution. The following table shows the three possible arrangements of two goats and one car behind three closed doors and the result of switching or staying after initially picking Door 1

.

Door 1 Door 2 Door 3 Outcome if switching Outcome if staying
Car Goat Goat Goat Car
Goat Car Goat Car Goat
Goat Goat Car Car Goat

.

Which means that in 2 out of 3 cases we would win the car by switching doors. Hence it would make perfect sense to always switch. To understand why this is happening do take into consideration that the event “staying” is composed by only one element while its complement by two (note that all elements are equiprobable).

.

Frequency of winning when staying/switching doors in a sequence of "Monty-Hall" games

Tagged , , , ,