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Terms in this set (15)
What is the sample space (S)?
The sample space S of a chance process is the set of all possible outcomes.
What is a probability model?
A probability model is a description of some chance process that consists of two parts: a sample space S and a probability for each outcome.
What is an event?
An event is any collection of outcomes from some chance process. That is, an event is a subset of the sample space. Events are usually designated by capital letters, like A, B, C, and so on.
What are the rules of probability models?
- The
probability of any event is a number between 0 and 1.
- All possible outcomes together must have probabilities whose sum is 1.
- If all outcomes in the sample space are equally likely, the probability that event A occurs can be found using the formula:
P(A) = number of outcomes corresponding to event A/total numbers of outcomes in sample space
- If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual
probabilities.
When are two events mutually exclusive (disjoint)?
Two events are mutually exclusive (disjoint) if they have no outcomes in common and so can never occur together.
- Turning left and turning right are Mutually Exclusive (you can't do both at the same time)
- Tossing a coin: Heads and Tails are Mutually Exclusive
- Cards: Kings and Aces are Mutually Exclusive
Complement rule
P(AC) = 1 - P(A)
How to remember the union and intersection symbols.
Hint: To keep the symbols straight, remember ∪ for union and ∩ for intersection.
Mutually Exclusive
- A and B together is impossible: P(A and B) = 0
- A or B is the sum of A and B: P(A or B) = P(A) + P(B)
(Addition rule for mutually exclusive events)
How to remember whether unions or intersection have more.
"Or has more ... than And"
Also ∪ is like a cup which holds more than ∩
Not Mutually Exclusive
- A or B is the sum of A and B minus A and B: P(A or B) = P(A) + P(B) − P(A and B)
(General Addition Rule for Two Events)
What is conditional probability?
The probability that one event happens given that another event is already known to have happened is called a conditional probability. Suppose we know that event A has happened. Then the probability that event B happens given that event A has happened is denoted by P(B | A).
What does it mean to say that two events are independent?
Two events A and B are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words, events A and B are independent if
P(A | B) = P(A) and P(B | A) = P(B).
General multiplication rule
The probability that events A and B both occur can be found using the general multiplication
rule
P(A ∩ B) = P(A) • P(B | A) where P(B|A) is the conditional probability that event B occurs given that event A has already occurred.
Multiplication rule for independent events
If A and B are independent events, then the probability that A and B both occur is
P(A ∩ B) = P(A) • P(B).
Conditional probability formula
P(B|A) = P(A ∩ B) / P(A).
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