Probability and Statistics (Basic)

[Pages:156]Probability and Statistics (Basic)

CK-12 Foundation

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Author Brenda Meery

Supported by CK-12 Foundation

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Contents

1 An Introduction to Independent Events 1.1 Independent Events

2 An Introduction to Conditional Probability 2.1 Conditional Probability

3 Discrete Random Variables 3.1 Discrete Random Variables

4 Standard Distributions 4.1 Standard Distributions

5 The Shape, Center and Spread of a Normal Distribution 5.1 Estimating the Mean and Standard Deviation of a Normal Distribution 5.2 Calculating the Standard Deviation 5.3 Connecting the Standard Deviation and Normal Distribution

6 Measures of Central Tendency 6.1 The Mean 6.2 The Median 6.3 The Mode

7 Organizing and Displaying Data 7.1 Line Graphs and Scatter Plots 7.2 Bar Graphs, Histograms, and Stem-and-Leaf Plots 7.3 Box-and-Whisker Plots

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Chapter 1

An Introduction to Independent Events

1.1 Independent Events

Learning Objectives

Know the definition of the notion of independent events. Use the rules for addition, multiplication, and complementation to solve for probabilities

of particular events in finite sample spaces.

What is Probability?

The simplest definition of probability is the likelihood of an event. If, for example, you were asked what the probability is that the sun will rise in the east, your likely response would be 100%. We all know that the sun rises in the east and sets in the west. Therefore, the likelihood that the sun will rise in the east is 100% (or all the time). If, however, you were asked the likelihood that you were going to eat carrots for lunch, the probability of this happening is not as easy to answer.

Sometimes probabilities can be calculated or even logically deduced. For example, if you were to flip a coin, you have a 50/50 chance of landing on heads so the probability of getting heads is 50%. The likelihood of landing on heads (rather than tails) is 50% or ?. This is easily figured out more so than the probability of eating carrots at lunch.

Probability and Weather Forecasting

Meteorologists use probability to determine the weather. In Manhattan on a day in February, the probability of precipitation (P.O.P.) was projected to be 0.30 or 30%. When meteorologists say the P.O.P. is 0.30 or 30%, they are saying that there is a 30% chance that somewhere in your area there will be snow (in cold weather) or rain (in warm weather) or a mixture of both. If you were planning on going to the beach and the P.O.P. was 0.75, would you go? Would you go if the P.O.P. was 0.25?

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