This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Probability is the mathematical measure of the likelihood of an event occurring. The sample space () is the set of all possible outcomes of an experiment, and an event (A) is a subset of these outcomes. The probability of an event A is given by: P(A) = Number of outcomes in ATotal number of outcomes in Probabilities always range from 0 (impossible event) to 1 (certain event), i.e., 0 P(A) 1. The complement of an event A, denoted A', is the event that A does not occur, and P(A') = 1 - P(A). The Addition Rule is used for the probability of event A or event B occurring, denoted P(A B). If A and B are mutually exclusive (cannot happen at the same time), then P(A B) = P(A) + P(B). Otherwise, for any two events: P(A B) = P(A) + P(B) - P(A B) where P(A B) is the probability of both A and B occurring. The Multiplication Rule is for the probability of event A and event B occurring. For independent events (where the occurrence of one does not affect the other), P(A B) = P(A) × P(B). For dependent events, we use conditional probability, P(A|B), which is the probability of A occurring given that B has already occurred: P(A|B) = (P(A B))/(P(B)) From this, the general multiplication rule is P(A B) = P(A|B) × P(B). Last free one today — make it count tomorrow, or type /upgrade for unlimited.