# Probability

• The concept of probability is a fundamental aspect in statistics. It’s used to quantify the likelihood or chances of an event taking place.

• Probability of an event is always between 0 and 1, inclusive. If an event is sure to happen, it’s probability is 1. If it is certain not to happen, the probability is 0.

• To calculate the probability of a single event, you divide the number of ways the event can occur by the total number of outcomes in the sample space. For example, in rolling a number cube, the probability of rolling a 1 is 1 (one way to roll a 1) divided by 6 (six total outcomes), or 1/6.

• Two events are considered independent if the outcome of one event does not affect the outcome of the other. For instance, flipping a coin and rolling a dice are independent events because the outcome of the coin toss does not impact the outcome of the dice roll.

• Probability can be determined empirically through repeated trials, or theoretically through an understanding of the situation.

• The addition rule of probability is used when you want to know the probability of any of several mutually exclusive events will occur. The rule is simply the sum of the probabilities of the events.

• The multiplication rule of probability is used when you’re looking at the probability of the intersection of two events. If the events are independent, the probabilities multiply.

• The concept of conditional probability is applied when the outcome of one event affects the outcomes of another. This is given as P(A | B), the probability of event A given event B has occurred, equals to the probability of A and B occurring together divided by the probability of event B. |

• When working with sets, Venn diagrams can provide a good visual representation to solve probability problems. It visually displays the relationships between different sets and their elements.

• A real life application of probability can be seen in predicting the weather, where meteorologists use probability to determine the chance of rain, snow, sunshine, etc.

• Understand the difference between mutually exclusive and non-mutually exclusive events. Mutually exclusive events cannot occur at the same time (like rolling a dice cannot result in both a 2 and a 4), while non-mutually exclusive events can occur together (like drawing a card that is both a heart and a queen).

• Make sure to understand and use various probability terms correctly like experiment, trial, outcome, sample space, event, favourable outcomes and so on.

• In cases where more than one event is considered, the concepts of independent and dependent events are important, along with understanding whether these multiple events are mutually exclusive or not.