Math / Data & Statistics

QuestionConditional Probability from Table (L2) Score: 0/5 Penalty: 1 off Show Examples
Question The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who has only completed high school is chosen at random, what is the probability that they are aged 50 or over? Round your answer to the nearest thousandth. \begin{tabular}{|c|c|c|c|c|c|} \hline & Age 20-29 & Age 30-39 & Age 40-49 & Age 50 \& over & Total \\ \hline High school only & 1377 & 505 & 594 & 1053 & 3529 \\ \hline Some college & 750 & 670 & 975 & 943 & 3338 \\ \hline Bachelor's degree & 1582 & 1059 & 1269 & 609 & 4519 \\ \hline Master's degree & 633 & 842 & 443 & 605 & 2523 \\ \hline Total & 4342 & 3076 & 3281 & 3210 & $\mathbf{1 3 9 0 9}$ \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? Find the chance that a person aged 50 or over has only finished high school. Watch out! Don't mix up the total number of high school graduates with all age groups!

STEP 2

1. Identify the relevant data
2. Calculate the probability

STEP 3

First, let's focus on the row for "High school only." We're interested in those who have completed only high school.

STEP 4

Next, locate the number of high school graduates aged 50 or over.
From the table, this number is 1053.

STEP 5

Now, we need the total number of high school graduates.
From the table, this is 3529.

STEP 6

To find the probability, we use the formula for conditional probability:
$P(\text{Aged 50 or over} \mid \text{High school only}) = \frac{\text{Number of high school graduates aged 50 or over}}{\text{Total number of high school graduates}}$

STEP 7

Plug in the numbers we identified:
$P(\text{Aged 50 or over} \mid \text{High school only}) = \frac{1053}{3529}$

STEP 8

Now, let's calculate the result:
$P(\text{Aged 50 or over} \mid \text{High school only}) \approx 0.298$

STEP 9

The probability that a randomly chosen high school graduate is aged 50 or over is approximately 0.298.

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Studdy Solution

STEP 1

What is this asking? Find the chance that a person aged 50 or over has only finished high school. Watch out! Don't mix up the total number of high school graduates with all age groups!

STEP 2

1. Identify the relevant data
2. Calculate the probability

STEP 3

First, let's focus on the row for "High school only." We're interested in those who have completed only high school.

STEP 4

Next, locate the number of high school graduates aged 50 or over.
From the table, this number is 1053.

STEP 5

Now, we need the total number of high school graduates.
From the table, this is 3529.

STEP 6

To find the probability, we use the formula for conditional probability:
$P(\text{Aged 50 or over} \mid \text{High school only}) = \frac{\text{Number of high school graduates aged 50 or over}}{\text{Total number of high school graduates}}$

STEP 7

Plug in the numbers we identified:
$P(\text{Aged 50 or over} \mid \text{High school only}) = \frac{1053}{3529}$

STEP 8

Now, let's calculate the result:
$P(\text{Aged 50 or over} \mid \text{High school only}) \approx 0.298$

STEP 9

The probability that a randomly chosen high school graduate is aged 50 or over is approximately 0.298.

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Studdy Solution

STEP 1

What is this asking? Find the chance that a person aged 50 or over has only finished high school. Watch out! Don't mix up the total number of high school graduates with all age groups!

STEP 2

1. Identify the relevant data2. Calculate the probability

STEP 3

First, let's **focus on the row** for "High school only." We're interested in those who have completed only high school.

STEP 4

Next, **locate the number** of high school graduates aged 50 or over.From the table, this number is **1053**.

STEP 5

Now, we need the **total number** of high school graduates.From the table, this is **3529**.

STEP 6

STEP 7

Plug in the numbers we identified:P(Aged 50 or over∣High school only)=10533529P(\text{Aged 50 or over} \mid \text{High school only}) = \frac{1053}{3529}P(Aged 50 or over∣High school only)=35291053​

STEP 8

Now, let's **calculate the result**:P(Aged 50 or over∣High school only)≈0.298P(\text{Aged 50 or over} \mid \text{High school only}) \approx 0.298P(Aged 50 or over∣High school only)≈0.298

STEP 9

The probability that a randomly chosen high school graduate is aged 50 or over is approximately **0.298**.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Identify the relevant data
2. Calculate the probability

First, let's focus on the row for "High school only." We're interested in those who have completed only high school.

Next, locate the number of high school graduates aged 50 or over.
From the table, this number is 1053.

Now, we need the total number of high school graduates.
From the table, this is 3529.

Plug in the numbers we identified:
$P(\text{Aged 50 or over} \mid \text{High school only}) = \frac{1053}{3529}$

Now, let's calculate the result:
$P(\text{Aged 50 or over} \mid \text{High school only}) \approx 0.298$

The probability that a randomly chosen high school graduate is aged 50 or over is approximately 0.298.