Probability Explained: Independent and Dependent Events

Probability Explained: Independent and Dependent Events

Probability is the measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means an event is impossible, and 1 means it is certain.

When dealing with multiple events, they can be classified into independent and dependent events based on how they affect each other.

1. Independent Events

Two events are independent if the outcome of one event does not affect the probability of the other event occurring.

Example:

• Tossing a coin twice: The result of the first toss (heads or tails) does not influence the result of the second toss.

• Rolling a die and drawing a card from a deck: The number on the die does not affect which card is drawn.

2. Dependent Events

Two events are dependent if the outcome of one event does affect the probability of the other event occurring.

Example:

• Drawing two cards from a deck without replacement: The probability of drawing an Ace on the second draw depends on whether an Ace was drawn first.

• Choosing a student from a class, then choosing another without replacing the first: The probability changes after the first selection.

Understanding whether events are independent or dependent is crucial for calculating probabilities accurately in real-world scenarios like medical testing, gambling, and risk assessment.