What is an event? Show
In probability, the set of outcomes from an experiment is known as an event. For instance, conducting an experiment on tossing a coin. The outcome in this experiment may be head or a tail - whatever takes place each time you toss the coin is the event.  Simple & Compound EventsA simple event is one that can only happen in one way - in other words, it has a single outcome. If we consider our previous example of tossing a coin: we get one outcome that is a head or a tail. A compound event is more complex than a simple event, as it involves the probability of more than one outcome. Another way to view compound events is as a combination of two or more simple events. Consider the probability of finding an even number less than 5. We have a combination of two simple events: finding an even number, and finding a number that is less than 5. EXAMPLE
Probabilities for Simple and Compound Events
The probability of an event occurring requires two known variables: the number of times the event can occur, and the total number of possible outcomes. We use the following formula to calculate probability: \[ Probability\ of\ event = \frac{Number\ of\ times\ it\ can\ occur}{Total\ number\ of\ possible\ outcomes} \] Let’s try some problems! 1. Kyle works at a local music store. The store receives a shipment of new CDs of various genres in a box. In the shipment there are 10 country CDs, 5 rock CDs, 12 hip hop CDs, and 3 jazz CDs. What is the probability that the first CD Kyle chooses from the box will be country? \( Step\ 1: \) How many Country CDs are there? number of times the event occurs \( \Longrightarrow 10 \) \( Step\ 2: \) How many CDs could Kyle choose from? total number of possible outcomes \( \Longrightarrow 30 \) \( Step\ 3: \) What is the probability that Kyle will choose a country CD first? \( \Longrightarrow P(E) = \frac{10}{30} \) applying the probability formula \( \Longrightarrow P(E) = \frac{1}{3} \) always reduce answer to lowest terms! 2. Kyle's store receives a new shipment of CDs in a box. In the shipment, there are 10 country CDs, 12 rock CDs, 5 hip hop CDs, and 3 jazz CDs. What is the probability that Kyle will select a jazz CD from the box, and then, without replacing the CD, select a country CD? This event consists of two simple events. \( Step\ 1: \) What is the probability of selecting a jazz CD? \( \Longrightarrow P(E_1) = \frac{3}{30} \) \( Step\ 2: \) What is the probability of selecting a country CD without replacing the jazz CD? \( \Longrightarrow \) What is our new total? \( \Longrightarrow 29 \) So the probability of selecting a country CD \( \Longrightarrow P(E_2) = \frac{10}{29} \) \( Step\ 3: \) What is the probability of the first event taking place, followed by the second event? \( \Longrightarrow P(E) = P(E_1) \times P(E_2) \) \( \Longrightarrow\ \ \ \ \ \ \ \ \ = \frac{3}{30} \times \frac{10}{29} \) \( \Longrightarrow\ \ \ \ \ \ \ \ \ = \frac{1}{29} \) (Note - Final answer is determined by just doing multiplying two events when both are independent events. We will discuss independent and dependent events later on!) What is a comparison between two or more similar events or things is known as?An analogy is a comparison made to show how two different things are similar, especially in limited ways. An analogy is a technique frequently used in literature to explain something by comparing it to something else (a literary device). There are several types of analogies you can make.
What type of correlation occurs when one variable increases while the other variable decreases quizlet?Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa.
What type of survey involves collecting information from a sample group of people?Data collection surveys collect information from a targeted group of people about their opinions, behavior, or knowledge. Common types of example surveys are written questionnaires, face-to-face or telephone interviews, focus groups, and electronic (e-mail or website) surveys.
In which of the following does the conclusion necessarily follow from the premises?There are two types of argument: deductive and inductive. A deductive argument is one in which it is claimed that the conclusion follows necessarily from the premises. In other words, it is claimed that under the assumption that the premises are true it is impossible for the conclusion to be false.
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When two events occur together at rates higher than probability, the relationship is called a(n)
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