Licensed Drivers in the United States In a recent year there...

Licensed Drivers in the United States In a recent year there were the following numbers (in thousands) of licensed drivers in the United States. $$ \begin{array}{lll}{} & {\text { Male }} & {\text { Female }} \\ \hline \text { Age 19 and under } & {4746} & {4517} \\ {\text { Age } 20} & {1625} & {1553} \\ {\text { Age } 21} & {1679} & {1627}\end{array} $$ Choose one driver at random. Find the probability that the driver is a. Male and 19 years or under b. Age 20 or female c. At least 20 years old

Licensed Drivers in the United States In a recent year there were the following numbers (in thousands) of licensed drivers in the United States.
$$
\begin{array}{lll}{} & {\text { Male }} & {\text { Female }} \\ \hline \text { Age 19 and under } & {4746} & {4517} \\ {\text { Age } 20} & {1625} & {1553} \\ {\text { Age } 21} & {1679} & {1627}\end{array}
$$
Choose one driver at random. Find the probability that the driver is
a. Male and 19 years or under
b. Age 20 or female
c. At least 20 years old

Key Concepts

Probability

Probability is the measure of how likely an event is to occur, calculated by taking the number of favorable outcomes and dividing it by the total number of possible outcomes. This concept is essential for analyzing random events in any context, including demographic data like licensed drivers.

Sample Space

The sample space is the complete set of all possible outcomes in a probability experiment. In this context, it represents all licensed drivers, which is used as the denominator when calculating the probability of any event.

Joint Probability

Joint probability refers to the probability of two or more events occurring at the same time. For instance, calculating the probability that a driver is both male and 19 years or under involves analyzing the intersection of these two conditions.

Union of Events

The union of events is used when calculating the probability that at least one of multiple events occurs. For example, determining the probability that a driver is either age 20 or is female requires combining the probabilities of these events, while adjusting for any overlap between them.

Complement Principle

The complement principle involves finding the probability of an event by subtracting the probability of its complement from one. This is useful in scenarios such as calculating the probability that a driver is at least 20 years old by considering the complement event (drivers under 20) and then determining the desired probability.

Transcript

00:01 Okay, so our problem is about license drivers.

00:03 So let's go to part 8.

00:05 Part 8 is asking us about the probability of them being a male, right? a male and being 19 years old or under, right? so i'm going to put years.

00:23 So let's see.

00:24 So here we got the probability of being male and less than or equals to 19 years of age.

00:37 I'm going to put age or years, right? so let's see.

00:41 So that will be, when we look at the table, we're going to end up with an amount that is 4 ,746 divided by the total amount of all the licenses held.

00:52 So 15 ,747.

00:56 And that's going to give us a probability of 0 .3101 ,000s.

01:02 Okay? so that's how you work.

01:04 On part a.

01:06 Now let's go to part b.

01:08 So for part b, this one is a little bit different.

01:11 This one is either they are 20 years of age, right? 20 years of age or they are female.

01:23 They are female.

01:24 Okay.

01:25 And i'm using this female symbol here.

01:28 So let's see.

01:29 So 20 years of age or female.

01:32 Okay.

01:32 So here we're going to use the addition rule number two.

01:38 So in order to get that, i'm going to start with 20 years of age, okay, 20 years of age, plus, right, and i'm going to add the probability of them being female...

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