The following data represent the number of driver fatalities...

The following data represent the number of driver fatalities in the United States in 2002 by age for male and female drivers: $$\begin{array}{|l|c|c|} \hline \text { Age} & \text { Male } & \text { Female }\\\hline \text { Under } 16 & 228 & 108 \\\hline 16-20 & 5696 & 2386 \\\hline 21-34 & 13,553 & 4148 \\\hline 35-54 & 14,395 & 5017 \\\hline 55-69 & 4937 & 1708 \\\hline 70 \text { and over } & 3159 & 1529 \\\hline\end{array}$$ (a) What is the probability that a randomly selected driver fatality who was male was 16 to 20 years old? (b) What is the probability that a randomly selected driver fatality who was 16 to 20 was male? (c) Suppose you are a police officer called to the scene of a traffic accident with a fatality. The dispatcher states that the victim is 16 to 20 years old, but the gender is not known. Is the victim more likely to be male or female? Why?

The following data represent the number of driver fatalities in the United States in 2002 by age for male and female drivers:
$$\begin{array}{|l|c|c|} \hline \text { Age} & \text { Male } & \text { Female }\\\hline \text { Under } 16 & 228 & 108 \\\hline 16-20 & 5696 & 2386 \\\hline 21-34 & 13,553 & 4148 \\\hline 35-54 & 14,395 & 5017 \\\hline 55-69 & 4937 & 1708 \\\hline 70 \text { and over } & 3159 & 1529 \\\hline\end{array}$$
(a) What is the probability that a randomly selected driver fatality who was male was 16 to 20 years old?
(b) What is the probability that a randomly selected driver fatality who was 16 to 20 was male?
(c) Suppose you are a police officer called to the scene of a traffic accident with a fatality. The dispatcher states that the victim is 16 to 20 years old, but the gender is not known. Is the victim more likely to be male or female? Why?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Relative Frequency

Relative frequency is an approach to probability where probabilities are estimated by dividing the count of occurrences of an event by the total number of relevant events. This method is applied when calculating the probabilities, such as the chance that a male fatality involves drivers within a specific age range or that a fatality in a certain age group is male.

Contingency Tables

Contingency tables are used to display the frequency distribution of variables and to summarize the relationship between them. In the example provided, the table organizes driver fatality counts by age group and gender, which facilitates the calculation of conditional probabilities by comparing counts across different categories.

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In this context, it is used to determine the likelihood of selecting an individual from a specific group (such as those aged 16 to 20 or male drivers) under a known condition, like being male or being in a particular age bracket.

Transcript

00:01 Alrighty, so i go ahead and took the liberty of creating a little spreadsheet here and also combining the totals because that's important as well okay, guys, so for part a what we need to understand for part a is they are specifically asking for a male driver there.

00:16 They're specifically asking for a mail driver.

00:18 So we're going to look in the column that talks about mail drivers there.

00:23 So we're going to be looking in the mail column.

00:25 So that's column b in our spreadsheet okay, so on this one, so they're asked for a specifically mail driver.

00:30 So they're asked for a specifically mail driver.

00:30 Is 16 to 20 years old.

00:31 So 16 to 20 if we look at the mail column is 5, 6, 9, 6.

00:37 And the probability that they are, so they have to be a male.

00:40 So they're looking for a male driver, and then the driver was 16 to 20 years old.

00:44 So all the male drivers total is 4 -1 -9 -6 -8.

00:48 And so we do that.

00:50 And it doesn't really say for decimal places of what to do.