Probability Concepts

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Probability Concepts by Mind Map: Probability Concepts

1. Definition of an Event is any outcome in an experiment

1.1. Simple Event: An event that can't be broken down into smaller events.

2. Sample Space = the set of all possible simple events. Sample Space of tossing a coin. S{HH, HT, TH, TT}

3. P(A) = Probability of event A occurring

3.1. P = Probability of

4. Relative Frequency of Probability: P(E) = # of times E occurs / total #of trials. For example, the P(of getting heads) = # of times Heads occurs / total number of trials

5. Complement: The complement of A is all the outcomes in S that are not included in A.

5.1. Rule: P(A) + P(Ā) = 1

5.2. P(Ā) = 1-P(A)

6. Compound Event: Two or more events

7. Addition Rule: P(A or B) = P(A) + P(B) - P(A and B). For example; find the probability of rolling a 6 or pulling an ace out of a standard deck of cards.

7.1. Keyword is OR

8. Mutually Exclusive: Cannot occur at the same time. For example, you can't flip a coin and land on heads and tails in the same event

8.1. Not Mutually Exclusive means something can occur at the same time.

9. Multiplication Rule: P(A and B) = P(A) x P(B/A) For example; find the probability of rolling a 3 and rolling a 5 when using dice.

9.1. Keyword is AND

10. When you are looking at the multiplication rule, you first need to see if the question is independent or dependent. Two events are independent if the first is not affected by the second.

11. Probability of at least one: P(@ least 1) = 1 - P(0) since the complement of 1 is 0.

12. Conditional Probability: P(A and B) = P(A) - P(B/A)

12.1. Keyword is GIVEN and IF

12.2. P(B/A)=P(A and B) / P(A)

13. Permutations: When the order does matter like 456 is not the same event as 654

14. Combinations: When the order doesn't matter. 678 is the same as 876