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Complements, Disjoint Events, and the Addition Rule

Complements, Disjoint Events, and the Addition Rule. Presentation 4.3 Overview. Probability Rules. The probability P(A) of any event is always a number between 0 and 1. The probability that you can read this is 1 (since we know for a fact you are reading it right now).

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Complements, Disjoint Events, and the Addition Rule

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  1. Complements, Disjoint Events, and the Addition Rule Presentation 4.3 Overview

  2. Probability Rules • The probability P(A) of any event is always a number between 0 and 1. • The probability that you can read this is 1 (since we know for a fact you are reading it right now). • The probability that the Jupiter is currently closer to the sun than Earth is 0 (it simply is not true). • The probability that you will be struck by lightning are 1/709260 or 0.0000014, rather close to 0. • According to Star Wars, the probability of successfully navigating an asteroid field are 1/3720 or 0.00027.

  3. Probability Rules • If S is the sample space in a probability model, the P(S) = 1. • That is, the probability that you get something from the sample space is 1, meaning it will happen. • This comes to you from the department of redundancy department.

  4. Probability Rules • The complement of any event A is the probability that the event A will NOT occur. • If the probability that it will snow today is 40%, then the probability that it will not snow is 60%.

  5. Probability Rules • Two events are disjoint (also called mutually exclusive) if they have no outcomes in common. • Examples from a Deck of Cards • Event A is choosing a face card and event B is choosing a 5. There is no way to choose a face card that is also a 5. These are disjoint or mutually exclusive. • Event A is choosing a 5 and event B is choosing a spade. Since there is a 5 of spades (an outcome in A and B) these are NOT disjoint or mutually exclusive.

  6. Probability Rules • Addition Rule • If A and B are disjoint (mutually exclusive), then: • P(A or B) = P(A) + P(B) • Example • What is the probability or choosing a 5 or a face card? • The probability of choosing a 5 is 4/52 since there are 4 fives in the deck of 52 cards. • The probability of choosing a face card is 12/52 since there are 12 face cards (J, Q, K in each of four suits) in the deck of 52. • Since they are mutually exclusive, • The probability is 4/52 + 12/52 = 16/52 or 0.3077.

  7. Complements, Disjoint Events, and the Addition Rule • This concludes this presentation.

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