# What is a Probability

Probability table is employed to tabulate all of the data determined for a standard values from that values new probabilities could be determined. The events also can be tabulated.

Probability Notation

If you can find n elementary events related to an random experiment and m of them are favourable to an event E, then the probability of E is denoted by P(E) and is defined to the ratio $\fracmn$.

=> P(E) = $\frac{\text{Number of Favourable to Event A}}{\text{Total Number of Outcomes}}$.

If an experiment has n similarly likely outcomes in S and N of them are the event A, then the theoretical probability of event A taking place is P(A) = $\fracnN$.

## How to Do Probability

Probability is a significant branch of math which fundamentally deals with the phenomena of chances or randomness of events. Probability of an event measures how likely it is expected to occur. An event is considered most likely if it has greater probability and least likely if it has lower probability. The probability of an event differs between 0 and 1. An event with probability 0 is an impossible event, although event having probability 1 is considered a certain event.

For a situation where several various outcomes are possible, the probability for any specific outcome is described as a fraction of all the possible final results. A sample space is a collection of all possible outcomes of a random experiment. A sample space might be infinite or finite. Infinite sample spaces may be discrete or continuous.

In everyday life, we speak informally about the probability of several event to happen. Example of a probability problem with a solution could be like this. While leaving the home in the morning on a cloudy day, one may have to choose to take an umbrella even when it is not raining because it may possibly rain later on in the day. The crucial types of probability problems are problems on conditional probability, problems on bayes theorem and problems on multiplication theorem.

## Probability Multiplication Rule

The addition rule assisted us solve problems when we carried out one task and wanted to learn the probability of two things occurring during that task. This lesson deals with the multiplication rule. The probability multiplication rule also deals with two events, however in these problems the events take place as a result of greater than one task (drawing two cards, rolling one die then another, pulling two marbles out of a bag, spinning a spinner twice, etc).

When asked to find the probability of A and B, we want to learn the probability of events A and B happening.

Consider events A and B. P(AᴖB)= P(A) P(B).

The Rule Means:

Assume we roll one die then another and want to locate the probability of rolling a 4 on the very first die and rolling an even number on the 2nd die. Notice in this problem we are not coping with the sum of both dice. We are just dealing with the probability of 4 on one die only and then, as an individual event, the probability of an even number on one die only.

P(4) = 1/6

P(even) = 3/6

So P(4ᴖeven) = (1/6)(3/6) = 3/36 = 1/12

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