The Chances of A Full House

The main objective of the popular game Bingo is to get a Full house. Well, there are other prizes and winnings based on getting something below a full house, but to attain a full house is the most coveted achievement in this game. So what exactly is a full house? No matter what country you are playing in, whether it's the American 75 ball bingo, or the European 90 ball bingo, a full house is reached when one is able to strike all the numbers present on his/her ticket. The striking out of the numbers is based on a randomly selected number called out by the "caller" in the Bingo hall/room. This events itself creates a scope for some simple probabilistic theory to come into play, regarding who, and how one can win a Full house.

Firstly, it should be clear to you that everyone present in the Bingo hall has an equal chance of getting a full house. That is because the calling of numbers in the Bingo hall is totally unbiased and random, and so is the distribution of numbers on the bingo card. Thus, for a hall of 50 people, the probability of winning is an equal share of 2% for everyone present. Likewise, for a gathering of 100 people, it would be 1% for everyone, which simply shows that more the number of people, lesser is the chance of winning a full house.

But I must tell you that this figure is wrong. Let us consider the standard 90 ball bingo, where there are numbers from 1-99. Also, there are 15 numbers present on each ticket. Therefore, the minimum number of calls required for one to get to a full house is 15, and the maximum, of course is 99. Now let us consider the ideal situation where one does win the full house in exactly 15 calls. For the first call, probability is 15/99, for the second, it is 14/98, and so on till the probability for getting a number of your choice on the 15th turn is 1/85. Multiplying all these terms, we get a total probability of 4*10-16%, which is extremely low and shows the harsh reality of impossibility. Getting away from the ideal situation can have more complicated mathematics, but with full consideration one can say that there exists high 99% of chance of you getting a full house after 65 turns.

This basically means that with an increase in the number of turns, the probability of one winning only rises. One can easily assimilate the thought that none of this was ever thought of when the game bingo was designed, way back in the 15th century. The simplistic nature of this game shows how excitement is immensely created with a hint of mathematical chance.


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