Question 2·Medium·Probability and Conditional Probability
The data on the coat color and eye color for 48 Himalayan kittens available for adoption were collected and summarized in the table below.
| Coat color | Deep blue | Light brown | Total |
|---|---|---|---|
| Cream-tortoiseshell | 16 | 16 | 32 |
| Chocolate | 12 | 4 | 16 |
| Total | 28 | 20 | 48 |
What fraction of the chocolate-colored kittens has deep blue eyes?
For two-way table problems that ask for "What fraction of [group] has [trait]?", immediately identify the group named after "of"—that group determines your denominator (row or column total). Then, find the cell where that group and the specified trait intersect; its count is your numerator. Form the fraction numerator/denominator, simplify if helpful, and then match it directly to the answer choice, making sure you did not accidentally use the total number of all individuals or the wrong row/column total.
Hints
Focus on the correct group
The question says "of the chocolate-colored kittens." Should your denominator be all 48 kittens, or just the kittens that are chocolate-colored?
Use the correct row and column
Look at the Chocolate row in the table. Which number in that row tells you the total number of chocolate-colored kittens?
Find the part of that group with deep blue eyes
Still in the Chocolate row, which number is under the Deep blue column? That is how many chocolate-colored kittens have deep blue eyes. Put this number over the total number of chocolate-colored kittens to form your fraction.
Desmos Guide
Enter the fraction you decided on
After you determine which count is the numerator ("number of chocolate-colored kittens with deep blue eyes") and which count is the denominator ("total number of chocolate-colored kittens"), type numerator/denominator into a Desmos expression line, such as a/b where a and b are your two counts. Look at the simplified fraction or decimal Desmos gives you.
Match the value to an answer choice
Compare the numerical value shown in Desmos to the values of each answer choice (you can type each option into Desmos as well if needed). Choose the option whose value matches the fraction you computed.
Step-by-step Explanation
Identify what the question is really asking
The question asks: "What fraction of the chocolate-colored kittens has deep blue eyes?"
That means we are looking within the group of chocolate-colored kittens only.
- The denominator should be the total number of chocolate-colored kittens.
- The numerator should be the number of kittens that are both chocolate-colored and have deep blue eyes.
Find the needed counts in the table
Look at the row labeled Chocolate in the table.
- In the Deep blue column of that row, the table shows 12. This is the number of kittens that are chocolate-colored with deep blue eyes.
- In the Total column of that same row, the table shows 16. This is the total number of chocolate-colored kittens.
Form the required fraction and match the choice
We want the fraction of chocolate-colored kittens that have deep blue eyes.
- Numerator: number of chocolate-colored kittens with deep blue eyes = .
- Denominator: total number of chocolate-colored kittens = .
So the desired fraction is , which matches choice D.