# decoding the monty hall game

*The Monty Hall Game Show A.K.A. Let's make a deal was a Television game show, it had three doors, with a sports car behind one of them and goats behind others, you make a choice, the host opens some other door which will turn out to be a goat, now you have a choice, either stick to previous choice or switch, simple, isn't it?*

## Is the probability 50%?

A typical observation of the situation might suggest that the probability is 50%, you have two choices, you have no idea where car is, so probability must be 50%, right

there are various factors while calculating probability we need to consider before calculating probability

- Is the event independent?
- Are the chances of one event greater than other?
- Are their other factors influencing probability?

## explanation of the biased probability

Any proficient mathematician, or a person with good knowledge of mathematics will be able to explain why the probability is not 50%.

### conditional probability

conditional probability is a concept of probability which deals with dependent events, ie. happening of one event affecting happening of other event, this is a really important concept as most of the events in real life are dependent events.

## actual probability of monty hall game

so, it turn out that the events are not equally likely, one is greater than other, what that means is, your chances of winning are greater if you switch rather than sticking to it.

The probability of winning on switching is **66%** while on sticking to choice is **33%**, So, next time you are playing this game, act smart.