AND/ OR Rules

AND/ OR Rules

AND Rules (Multiplication Rule)

  • The AND rules in probability are often referred to as the Multiplication rules.

  • When events are independent, the probability that both events will happen can be calculated by multiplying the probabilities of the individual events. For example, if you’re flipping two coins, the probability that both will land on heads is calculated as: P(First Coin is Heads) x P(Second Coin is Heads).

  • We assume that the outcome of the first event does not change the probability of the second event occurring when events are independent. This is a key property of independent events.

  • For dependent events (where the outcome of the first event does affect the outcome of the second), we must adjust the probability of the second event based on the outcome of the first event.

  • With dependent events, it’s necessary to work out the initial probability of the first event happening, and then the conditional probability of the second event happening, given that the first event has happened. Then multiply these probabilities together to find the overall probability.

OR Rules (Addition Rule)

  • The OR Rules in probability are also known as the Addition rules.

  • When events are mutually exclusive (i.e., both cannot happen at the same time e.g., a card drawn from a deck can’t be both a heart and a spade), the probability that either event will happen is calculated by adding their individual probabilities.

  • For instance, the probability that a card drawn from a deck is either a heart or a spade is calculated as: P(Heart) + P(Spade).

  • Remember, in the case of mutually exclusive events, the outcome of one event does not influence the outcome of the other event.

  • If the events are not mutually exclusive (i.e., can both happen at the same time, such as drawing a red card or drawing a heart from a deck of cards), then we need to remove the duplication when we add the probabilities. In other words, P(A or B) = P(A) + P(B) - P(Both A and B).

  • Be cautious when determining whether events are mutually exclusive or not, as it’s very crucial to applying the correct rule.

Practice and understand these rules well. They form the foundation of most probability question solving techniques.