# Probability

**Probability**

In the context of quantitative ability, probability refers to the likelihood of a particular event or outcome occurring. It is a branch of mathematics that deals with uncertainty and randomness. Probability is expressed as a value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to happen.

In quantitative ability tests, probability questions may involve various scenarios, such as tossing a coin, rolling a die, drawing cards from a deck, or solving real-life problems that involve uncertain outcomes. Some common concepts and terms related to probability in quantitative ability include:

**Experiment:** The process or activity that leads to uncertain outcomes. For example, tossing a coin or rolling a die is an experiment.

**Sample Space:** In probability theory, the sample space is the set of all possible outcomes of an experiment or a random process. For example, when rolling a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.

**Event:** A subset of the sample space that represents a particular outcome or set of outcomes. For example, getting an even number when rolling a die is an event, and it corresponds to the set {2, 4, 6}.

**Probability of an Event:** The likelihood of an event occurring, usually denoted by P(event). It is calculated as the ratio of the number of favorable outcomes to the total number of outcomes in the sample space.

**Independent Events:** Two or more events are independent if the occurrence of one event does not affect the occurrence of the other. The probability of the intersection of independent events is the product of their individual probabilities.

**Dependent Events:** Two or more events are dependent if the occurrence of one event affects the occurrence of the other. The probability of the intersection of dependent events is the product of the conditional probabilities.

**Complementary Events:** The complement of an event A (denoted by A') is the event that A does not occur. The probability of an event A and its complementary event A' together is always 1. In other words:

P(A) + P(A') = 1

where P(A) is the probability of event A, and P(A') is the probability of its complementary event A'.

**Examples:**

Example 1:

Coin Toss: What is the probability of getting heads when flipping a fair coin?

Here, the sample space is {Heads, Tails}, and the probability of getting heads is 1/2 (since there is one favorable outcome out of two possible outcomes).

Dice Roll: What is the probability of rolling a 3 with a standard six-sided die?

The sample space is {1, 2, 3, 4, 5, 6}, and the probability of rolling a 3 is 1/6 (one favorable outcome out of six possible outcomes).

Example 2:

Spinner Game: In a game with a spinner divided into four equal sections (A, B, C, D), what is the probability of landing on section A?

The sample space is {A, B, C, D}, and the probability of landing on section A is 1/4 (one favorable outcome out of four possible outcomes).

Probability plays a crucial role in various fields, including statistics, economics, finance, and science. In quantitative ability tests, understanding probability concepts is essential for solving problems related to data analysis, decision-making, and making predictions based on uncertain information.