**Probability **is the measure of how probable a happening, occurrence or event is to happen out of the number of predictable outcomes. Many events can't be foreseen and predicted with total inevitability. The best we can say is how probable they are to happen, using the concept of probability. Reasoning and judgment are the key points before calculating probabilities even with a certain point of uncertainty. Probability is the chance of one or more incidence by the number of probable consequences. Therefore, let's consider this example where you're trying to find the prospect of rolling a three on a six-sided die. Here, "Rolling a three" is the happening or occurrences, and as we know that a six-sided die can land in any one of six numbers ( either a one, a two , a three, a four , a five or a six) the number of results or outcomes is six.

Example 1: Tossing a Coin

When a coin is tossed, there are two possible outcomes:

- heads (H) or
- tails (T)

We conclude that the chance of the coin landing **H **is $\frac{1}{2}$** **and** T** is $\frac{1}{2}$.

Example 2: A pot contains 4 red marbles, 6 blue marbles and 10 yellow marbles. If a marble is drawn from the jar randomly, what is the likelihood that the marble is blue?

"Choosing a blue marble" is an event, and the number of outcomes is equal to the total number of marbles in the jar, 20.

Spontaneously, the mathematical concept of probability deals with arrangements that occur in random proceedings.

Computing the probability of several events is a fact of breaking the problem down into distinct probabilities. The probability of multiple events occurring one after another is given when the probability of each occasion is multiplied by one another. A test has unplanned outcome if the consequence of the analysis can't be forecasted with complete certainty. An event is a set of possible outcomes of an analysis it occurs as an outcome of an attempt if it comprises the actual outcome of that experiment. Individual occurrence involving an event are said to be advantageous to that event. Events are assigned an amount of certainty which is called probability (of an event.)

**The Probability Rules:**

- Ensure that two outcomes must be jointly exclusive. Which means they both cannot occur at the same time.
- Allocate a probability that is a non-negative number. If it arrives at a negative number, recheck the calculations.
- The probability of all possible events needs to add up to 1 or 100%. If the chance of all possible events doesn't add up to 1 or 100%, there is a mistake made because a possible event is left out.
- Signify probability of an impossible outcome with a 0. Which means that there is no chance of an event happening.

Sometimes you can measure a probability with a number like "30% chance of rain", or you can use words such as impossible, likely, possible, unlikely , even chance and certain.

- Gather data by random mechanism.
- Use probability to predict outcomes of experiments under assumptions.
- Calculate probability of error larger than given amount.
- Work out probability of given departure between prediction and outcomes under assumption.
- Decide whether or not assumptions likely realistic.

Statistics is closely related to probability theory. Students use statistics to work out the probability, the chance that a certain event will occur: if you want to know the chance that it will rain during holiday, you think of how many times it has rained within a year. Since this number is very small, you presume that the chance of raining is small. You do a very meek statistical study of the data regarding rain and used it to work out a probability.

But have you noticed that things can also work the other way around: you can use intellectual probabilities to help you with stats. Say for example you want to test whether a die that is used in a gaming club is fair. To do this, you toss the die a number of times and record the results. You then reason like: if the die is fair, then each number should be correspondingly likely. There are six numbers, thus each number should come up in 1/6 of the cases. What you are doing is relating the actual die with an idyllic die: if your gaming club die does give you each number in roughly 1/6 of all throws, you agree that it is fair.

Probability therory is important when it comes to calculating statistics. You use probability theory to calculate the probability that the outcome occurred by chance. Statistics, and the fundamental theory of probability, are evidently useful for opinion investigators and professional bettors.

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