# Probability Chapter 3

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Independent Events: Two events are said to be independent when probability of occurrence of one event is not affected by occurrence or nonoccurrence of other event. An example of two independent events is as follows; say you rolled a die and flipped a coin. The probability of getting any number face on the die in no way influences the probability of getting a head or a tail on the coin.

Dependent Events: When two events are said to be dependent, the probability of one event occurring influences the likelihood of the other event.  For example, if we were to draw a two cards from a deck of 52 cards. If on your first draw we had an ace and we put that aside, the probability of drawing an ace on the second draw is greatly changed because we drew an ace the first time.

Joint Probability: Joint probability is defined as the probability of both A and B taking place, and is denoted by P(A∩B). This calculation is sometimes referred to as the multiplication rule of probability.

Multiplication Rule of Probability:  The multiplication rule is a way to find the probability of two events happening at the same time.

Where P(B|A) means “the probability of A happening given that B has occurred” that means this term in above equation tries to quantify the effect of the occurrence of event A on the occurrence of event B.

The multiplication rule can further be modified based on the condition of dependence/Independence of events.

Dependent Events: In case the two given events A and B are dependent then multiplication rule will be:

Independent Events: If AA and BB are two independent events in a probability experiment, then the probability that both events occur simultaneously is: