Question\begin{problem}
In a survey, 46,139 women were asked how many children they had. The results were as follows:
\begin{center}
\begin{tabular}{|c|r|}
\hline
\textbf{Number of Children} & \textbf{Number of Women} \\
\hline
0 & 12,516 \\
1 & 7,406 \\
2 & 11,285 \\
3 & 7,106 \\
4 & 3,793 \\
5 & 1,810 \\
6 & 920 \\
7 & 523 \\
8 or more & 780 \\
\hline
\textbf{Total} & 46,139 \\
\hline
\end{tabular}
\end{center}
What is the probability that a sampled woman has three children? Round your answer to four decimals.
The probability that a sampled woman has three children is .
\end{problem}
Studdy Solution
STEP 1
What is this asking?
Out of a bunch of women surveyed, some had 3 kids.
What are the chances of picking a woman at random who had 3 kids?
Watch out!
Don't mix up the number of women with 3 kids with the total number of women surveyed.
STEP 2
1. Find the relevant numbers.
2. Calculate the probability.
3. Round the result.
STEP 3
We're looking for the probability of picking a woman with **3 children**.
Let's find that number in the table.
Boom! It's **7,106** women.
STEP 4
Now, let's find the **total number** of women surveyed.
That's the total at the bottom of the table: **46,139** women.
STEP 5
Probability is all about comparing the **specific event** (having 3 kids) to the **total possibilities** (all the women surveyed).
STEP 6
The probability is calculated by dividing the **number of women with 3 children** by the **total number of women**.
Let's do it!
STEP 7
Calculating the fraction:
STEP 8
The problem asks us to round to **four decimal places**.
Looking at our result , the fifth decimal place is a 2, which is less than 5, so we round *down*.
STEP 9
Our rounded probability is **0.1540**.
STEP 10
The probability that a sampled woman has three children is **0.1540**.
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