Its more like an observation rather than a fact.
So, here’s the thing which I am pretty sure most people haven’t observed!
Yesterday, I was watching the all time Bollywood classic Andaz Apna Apna. There’s a scene in the movie where Robert and Bhalla offer juice to everyone on the occasion of Robert’s (fake) birthday.
Unknown to everyone else, one of the glasses is poisoned and is given to Raveena. But before anyone could drink it, Amar jumbles up the glasses in the process of recreating a football match and thus Robert and Bhalla get confused as to which one is the poisoned glass.
So, in order to find out who has the poisoned glass, they wait till everyone takes a sip but unfortunately for them, no one gets the poisoned glass. So, what Bhalla does next is the most amazing thing about my observation!
He exchanges his glass with Robert’s and thus end up increasing his probability of getting a poisoned glass.
This, my friends, is a classic example of Monty Hall problem!
From wikipedia :
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall.
It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990:
“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?”
Vos Savant's response was that the contestant should switch to the other door. Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance.
Hence Bhalla switched his glass thus increasing his probability of getting a poisoned glass!