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Discrete Mathematics for Computing (Draft)

Section 6.2 Consecutive Events: Independence or Dependence

In the previous section, we were interested in a single outcome associated with a single (atomic) process. We learned and practiced how to compute probabilities associated with outcomes/events that were determined by multiple restrictions (drawing a red card and a face card) as well as outcomes that were described by "options" (drawing a red card or a face card).
In this section we’ll be interested in outcomes associated with distinct processes. For example, perhaps we roll a die and then draw a card from a deck. Similarly, perhaps we deal two cards from a deck rather than a single card. In this latter example, we can consider the drawing of each individual card as an atomic process). In the first example, the outcome of the die roll doesn’t impact the drawing of a card -- these events are independent. In the second example, however, the result of the first card dealt does impact the probabilities associated with what our second card will be -- the dealing of these two cards are dependent events.
Let’s dig into the section to learn more and gain some practice.

Subsection 6.2.1 Consecutive Events, Independence/Dependence, and Probabilities

Sometimes we are interested in the probabilities of outcomes associated with several distinct processes. For example, we may want to know the probability of being dealt an two Aces
In this section you learned, and practiced with...