With conditional probability events, event B will only occur given the knowledge that an event A has already occurred. This probability is written as (B/A), a notation implying that the probability of B given A. For example; suppose you need to draw two similar cards in order to win when playing a card game. Of the 52 cards, there are 13 cards in each suit. Suppose you first draw a heart, and you now wish to draw a second heart, there are now only 12 hearts remaining in a deck of 51 cards. So your conditional probability will be P (Draw second heart |First card a heart) = 12/51.
The probability of independent events states that the occurrence of one event is not affected by the other. Given that event B occurred gives no information whether event A occurred or not, therefore the probability assigned to A may not be conditioned by the knowledge that B occurred, hence P(A)(B)=P(A). For example; when tossing a coin getting tails or heads does not depend on outcome of the tosses done previously. Each toss is an independent event.
Two events are considered mutually exclusive if they cannot take place at the same time, that is, they are completely disjoint events. If the two events are disjoint, then there is no probability of them occurring at the same time. The probability of either occurring is the sum of the probabilities of each occurring that is; P (A or B) = P (A) + P (B). For example, in a high school consisting of 25 percent juniors, 15 percent seniors and 60 percent students of other graders, the relative frequency of students who are either seniors or juniors is 40 percent. You can add the relative frequencies of juniors and seniors because no student can be both junior and senior. That is; P (Junior or Senior) = 0.25 + 0.15 which equals 0.40.
A set of jointly exhaustive events has all the possible elementary events for an experiment. For example; when rolling a die, the outcomes 1, 2, 3, 4, 5 and 6 are jointly exhaustive if they include the entire range of possible outcomes.