Probability

Probability

Objectives

1. Construct Probability Models

2. Compute Probabilities of Equally Likely Outcomes

3. Find Probabilities of the Union of Two Sets

4. Use the Complement Rule to find Probabilities

Multiple Choice

The following M&M colors are in the bowl:
4 yellow, 6 orange, 3 green, 5 blue, and 2 brown.

What is the probability of selecting a green M&M?

•  $\frac{1}{5}$  

•  $\frac{3}{10}$  

•  $\frac{3}{20}$  

•  $\frac{1}{10}$  

Multiple Choice

The following M&M colors are in the bowl:
4 yellow, 6 orange, 3 green, 5 blue, and 2 brown.

What is the probability of selecting a yellow M&M?

•  $\frac{1}{5}$  

•  $\frac{3}{10}$  

•  $\frac{3}{20}$  

•  $\frac{1}{10}$  

Multiple Choice

What is the probability of spinning a number less than 5?

•  $\frac{1}{2}$  

•  $\frac{2}{3}$  

•  $\frac{5}{6}$  

•  $\frac{1}{3}$  

Multiple Choice

What is the probability of spinning a number greater than 5?

•  $\frac{1}{2}$  

•  $\frac{2}{3}$  

•  $\frac{5}{6}$  

•  $\frac{1}{6}$  

Multiple Choice

What is the probability of NOT rolling a 7 on a single regular die?

•  $\frac{1}{2}$  

•  $0$  

•  $\frac{5}{6}$  

•  $\frac{6}{6}$  

Definition of Probability

it is an area of mathematics that deals with experiments that yield random results, yet admit a certain regularity.

Results of experiments over long periods produce patterns that enable us to make predictions.

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Probability Models

A probability model has two components

1) A sample space

2) An assignment of probabilities

Properties of Probability

1) The probability assigned to each outcome is nonnegative.

2) The sum of all probabilities equals 1.

Multiple Select

Which tables represent a probability model?

• (a)

• (b)

• (c)

• (d)

Constructing a Probability Model

An example consists of rolling a fair die once. A die is a cube with each face having 1, 2, 3, 4, 5, or 6 dots on it. Construct a probabilty model for it.

Multiple Choice

An experiment consists of tossing a coin. The coin is weighted as so that heads {H} is three times as likely to occur than tails {T}.

What are the probabilities of each outcome?

• $P\left(H\right)=\frac{1}{2}$
  
  $P\left(T\right)=\frac{1}{2}$
  

• $P\left(H\right)\ =\ \frac{1}{4}$
  
  $P\left(T\right)=\frac{3}{4}$
  

• $P\left(H\right)=\frac{3}{4}$
  
  $P\left(T\right)=\frac{1}{4}$
  

• $P\left(H\right)\ \frac{3}{4}$
  
  $P\left(T\right)=\frac{1}{2}$
  

Define Event

Probability for Equally Likely Outcomes

Example of equally likely outcomes