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**Chapter 1:Independent and Dependent Events**

Statistics Chapter 1:Independent and Dependent Events

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Independent Events

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**What is in a word? What is dependent? What is independent?**

Any real-life examples? Any math examples? What is independent?

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Venn diagrams A graphic organizer that shows a visual representation for all possible outcomes of an experiment and the events of the experiment in ovals. Can you draw one? Can you create an example and name the sample space?

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Independent Events Independent events are those events which do not depend on each other. Can you think of some examples? Choosing an ace from a deck of cards and rolling a 6 on a dice. In a Venn-diagram independent events are represented as those events that occur in both sets.

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**Symbols Two main symbols used with Venn-diagrams:**

U = union or the outcome is in either of two sets n = intersection or the outcome is in both sets Example: What is P U Q? What is P n Q?

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Multiplication rule Used to find the probability of two events occurring. Examples: What is the probability of tossing two coins and them both landing on heads? What is the probability of tossing two coins and one landing on heads, the other on tails?

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**Examples Suppose 1 student is chosen at random:**

Gender University Community College Total Males 28 56 84 Females 43 37 80 71 93 164 Examples Suppose 1 student is chosen at random: What is the probability that the student is female? What is the probability that the student is going to university? Suppose 2 students are chosen at random, assume it is not possible to choose the same student What is the probability that the first person chooses a student who is female and the second person chooses a student who is going to a university?

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Dependent Events

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Dependent events Dependent events are those events which the probability of the second event occurring is affected by the first event occurring. Can you think of some examples? Dependent events usually are classified with the words “without replacement”

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Multiplication Rule Used to find the probability of two events occurring. Examples: What is the probability of choosing a seven out of a deck of cards, then choosing another seven out of a deck of cards without replacement? What is the probability of choosing a seven followed by another seven out of a deck of cards, with replacement?

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**Example A box contains 5 red marbles and 5 purple marbles.**

What is the probability of drawing 2 purple marbles followed by 1 marble in succession without replacement?

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**Mutually Inclusive and mutually exclusive events**

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**More terms AND (n) – same thing as intersection**

the outcome is in both sets OR (U) – same thing as union outcome is in either of two sets

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**Mutually exclusive Events**

To be mutually exclusive events, two events cannot occur at the same time. They can have no common outcomes Can you think of some mutually exclusive events? Example: Picking a number between 1 and 10 that is both even and odd.

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**Venn diagram Example: What is P(A or B)? What is P(A and B)**

P(A or B) = P(A) + P(B) OR means union, what is in either of the two sets What is P(A and B) P(A and B) = overlap AND means intersection, what is common in both

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**Mutually Inclusive events**

To be mutually inclusive events, two events can occur at the same time. Can you think of some mutually inclusive events? Picking a number from 1 to 10 that is less than 4 and picking an even number.

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Addition principle Use the addition principle when finding the probability of mutually inclusive events. P(A U B) = P(A) + P(B) – P(A n B) P(A n B) = 0 for mutually exclusive events

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Example What is the probability of choosing a card from a deck of cards that is a club or a ten?

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Example What is the probability of choosing a number from 1 to 10 that is less than 5 or odd?

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Example 2 fair dice are rolled. What is the probability of getting a sum less than 7 or a sum less than 4?

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The real Question… Are there any questions?

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