Probability

Probability is a branch of mathematics that deals with calculating the likelihood of a given event’s occurrence, which is expressed as a number between 1 and 0. Here are some key concepts and terms in probability:

1. Experiment: A procedure that produces outcomes. For example, rolling a die.
2. Sample Space (S): The set of all possible outcomes of an experiment. For a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.
3. Event (E): A subset of the sample space. For example, getting an even number when rolling a die: {2, 4, 6}.
4. Probability of an Event (P(E)): A measure of the likelihood that an event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes. For example, the probability of rolling an even number on a six-sided die is 3/6 or 0.5.

Basic Probability Rules

1. Addition Rule: For two mutually exclusive events, A and B, the probability that A or B occurs is P(A or B) = P(A) + P(B).
2. Multiplication Rule: For two independent events, A and B, the probability that both A and B occur is P(A and B) = P(A) * P(B).
3. Complementary Rule: The probability that an event does not occur is 1 minus the probability that it does occur: P(A’) = 1 – P(A).

Example Problems

1. Simple Probability: What’s the probability of drawing a red card from a standard deck of 52 cards?

• There are 26 red cards in a deck.
• P(Red) = 26/52 = 1/2 or 0.5.

1. Conditional Probability: What’s the probability of drawing a king given that you have drawn a face card?

• There are 12 face cards (Jack, Queen, King of each suit) in a deck.
• There are 4 kings.
• P(King | Face card) = 4/12 = 1/3 or approximately 0.333.

Would you like to explore more specific topics or problems in probability?