Probabilities
As the name suggests, probability refers to the chances of something happening given a set of conditions. Using a simple example, we might try to determine the probability of boys born in a given hospital of 100 expecting mothers. Here, the likelihood of a mother to deliver either a boy or a girl is 50/50, meaning that there is a 50 percent chance that the expecting mothers can either bear a boy or a girl. This is a simple probability. However, there are contexts where determining the probability of a given outcome is more complicated. For instance, in situations where the expected outcome is more than two, casting dice with six sides. Here, the likelihood of one outcome occurring is reduced significantly. Hence, more elaborate calculations are needed. Statistics govern probability events, and there are various types and dimensions, as will be visited below.
- Conditional
As the name suggests, conditional probability is slightly different from simple probability. Conditional probability refers to the chance of a given outcome given a set of rules or conditions (P(A|B)). For instance, we may be asked what probability of a person getting sick if they ate an expired cheese. Here, the outcome under investigation (getting sick) is based on the condition that bad cheese is consumed.
- Marginal
Unlike conditional probability, which is the possibility of an event occurring given a conditional event, the events of marginal probability do not depend on specific events or variables. In short, the probability of an outcome is not predicated on the variables; this is why marginal probability is often thought of as “unconditional probability.” For example, the probability of picking the ace of spades from a deck does not depend on any other variable except chance. Picking the ace of spades from a deck is purely based on probability and does not depend on other events or variables.
- Intersection
In simple probability, investigations usually involve determining the possibility of one event occurring with respect to another event. When we talk about an intersection in probability, it means the likelihood of both events occurring simultaneously, and the symbol denotes it “∩.” In a formula, this would be represented as P (A ∩. B). For instance, determining the possibility of picking an even number and number greater than five in the distribution of 1 to 10. Here, what is being investigated is the likelihood that the number picked is both an even number and greater than 5. Possible picks that fit these specifications are 6, 8, and 10; the three numbers are both even and greater than 5.
- Union
When it comes to the union of events in probability, it refers to the likelihood of either event “A” or even “B” occurring independently or together (both A and B occurring), and the symbol denotes it “∪.” In a formula, this would be represented as P (A ∪ B), where events A, or B, or both can occur.
- Independent and mutually exclusive event probabilities
In probability, when there is no chance of two events occurring together, it is said to be mutually exclusive. Mutually exclusive events are independent of other variables or events. For instance, the chance of landing on “heads” in a coin toss does not depend on the “tail.” Landing on “heads” occurs independently from the “tail” side; the occurrence of one event does not influence the occurrence of the other.
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