A local postal carrier distributes firstclass letters,...

A local postal carrier distributes firstclass letters, advertisements, and magazines. For a certain day, she distributed the following numbers of each type of item. $$ \begin{array}{lccc} \\ \text { Delivered to } & \text {First-class letters } & \text { Ads } & \text { Magazines } \\ \hline \text { Home } & 325 & 406 & 203 \\ \text { Business } & 732 & 1021 & 97 \end{array} $$ If an item of mail is selected at random, find these probabilities. a. The item went to a home. b. The item was an ad, or it went to a business. c. The item was a first-class letter, or it went to a home.

A local postal carrier distributes firstclass letters, advertisements, and magazines. For a certain day, she distributed the following numbers of each type of item.
$$
\begin{array}{lccc}
\\
\text { Delivered to } & \text {First-class letters } & \text { Ads } & \text { Magazines } \\
\hline \text { Home } & 325 & 406 & 203 \\
\text { Business } & 732 & 1021 & 97
\end{array}
$$
If an item of mail is selected at random, find these probabilities.
a. The item went to a home.
b. The item was an ad, or it went to a business.
c. The item was a first-class letter, or it went to a home.

Key Concepts

Probability

Probability is a measure that quantifies how likely an event is to occur, usually expressed as a ratio of favorable outcomes to the total number of outcomes. It provides a framework for analyzing uncertain situations by assigning numbers between 0 and 1 to possible events, where 0 means the event never happens and 1 indicates certainty.

Sample Space

The sample space is the set of all possible outcomes in a probability experiment. It serves as the foundation for probability calculations since each event's likelihood is determined by considering how many outcomes in the sample space align with the event in question.

Counting Techniques

Counting techniques involve methods for determining the number of outcomes in the sample space as well as the number of favorable outcomes for an event. This often includes straightforward counting, addition, or more advanced combinatorial methods, and is essential to accurately computing probabilities.

Addition Rule of Probability

The addition rule of probability is used when determining the probability of the union of two events, particularly when the events are not mutually exclusive. It states that the probability of either event occurring is the sum of the individual probabilities minus the probability of the intersection of the events, which corrects for any overlap counted twice.

Transcript

0:00 So this is a two -way table.

00:01 What do i know about this two -way table? well, local postal carriers distributes three different types of things.

00:07 First class letters, advertisements and magazines, so the type of distribution, and then either to a home or a business.

00:16 Okay.

00:16 So first thing i'm going to do, given these numbers, for example, 325 are delivered to a home in our first class letters, 406 or ads delivered to a home, and then 203 are magazines delivered to a home.

00:29 I could find the total of everything delivered to a home by adding these three numbers.

00:35 So 325 plus 406 plus 203 is 934.

00:41 And then my other numbers are for my business, 732 first class letters, delivered to a business, so on and so forth.

00:50 Find the total of this row, which will be approximately 1850.

00:56 And then from this i could find the total number.

01:00 I could add the total total, 934 plus 1850, 2784.

01:06 And then let's finish this table.

01:07 What's the total of first class letters? why have 325 delivered to a home, 732 delivered to a business.

01:14 So 1057.

01:16 For ads, add that column, 1427.

01:20 And then for magazines add to a 3 in 97, 300.

01:24 Just to double check that this adds to the total total, plus 1427 plus 1057.