What is probability explain in detail?

Answer 1

Probability is the likelyhood that some particular outcome will occur. It is expressed as a number between 0 and 1, with 0 meaning there is no likelyhood at all, and with 1 meaning it is guaranteed to happen.

A simple example is the flipping of a coin. There is a 0.5 probability of getting heads, and there is a 0.5 probability of getting tails. Assuming a fair coin.

Another example is a standard deck of 52 playing cards. There is a 0.25 probability of getting a Heart, and there is a 0.75 probability of not getting a Heart.

Probability is not an exact predictor of outcome. If you flipped a coin 100 times, for instance, you would expect about 50 of the throws to be heads, but you will not get that exact outcome. Even if you throw the coin 10 million times, you will not get exactly 5 million heads. What happens is that, as the number of trials increases, the closer the experimental results are to the theoretical probability.

One important factor of probability is that the sum of the probabilities of all possible outcomes is equal to the number of all possible trials. Stated another way, the sum of all probabilities is always equal to exactly 1. Stated yet another way, the probability that something is going to happen is 1.

This can get complicated, particularly when the number of outcomes is large. Take the New York State lottery game Lotto, for instance - you pick 6 numbers out of 59 - there are so many popssible results that special mathematics (the science of permutations and combinations) is used to do that calculation. In this case, there are 45,057,474 combinations of 59 things taken 6 at a time, so the odds of winning the jackpot on one game is 1 is 45,057,474 or about a probability of 0.00000002194. Another way to say this is that the probability of not winning the jackpot is about 0.9999999778.

I have only scratched the surface on this topic. Any other contributor is, as always, welcome to refine this answer.