mathematics

Statistics

probability

Lottery

Winning by luck

Likelihood Function

What are the odds?

Why is it so silly to buy a lottery ticket? Why are some events considered less likely to happen than the others? How do we make sense of the random nature of events around us?

We know that nothing is a hundred percent predictable- there is always some chance that things may not go as planned. For example, I buy some stocks or shares because they seem to be doing well. However, we cannot say with a hundred percent certainity that they will continue to do so. At best, we can predict the most likely trend for our shares. Thus, by studying statistics, we find the “likelihood function” for a given event to occur given the external parameters.

Probability is the study of likelyhood of events happening. For example, a probability of 100% implies the event will always happen- if I roll a dice, the number will be between 1 and 6. A probability of 0% implies that the event cannot happen- I cannot pick a card reading 12 (of any suite) from a standard deck of cards. Further, the events may be mutually exclusive : If event A occurs, event B cannot, and vice versa. For example, in a coin toss, coin landing heads and coin landing tails are mutually exclusive. The events may be independent: event A does not effect event B in any way at all. There are three fundamental axioms of Probability, which require a conceptual understanding of set theory.

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