Certainly, let's break down the problem step by step.
First, we will analyze the given data:
1. Tina has a total of 48 rabbits.
2. Out of these, 32 rabbits are male.
3. Therefore, the number of female rabbits is \( 48 - 32 = 16 \).
4. We know that 9 of the female rabbits are black.
5. Also, 14 of the male rabbits are white.
### Part a) Constructing the Two-Way Table
We need to categorize the rabbits by both color and gender. We'll complete the two-way table by filling in the known information and deducing the unknowns.
#### Step 1: Determine the number of white female rabbits.
- Total female rabbits: 16
- Black female rabbits: 9
- Thus, white female rabbits \( = 16 - 9 = 7 \)
#### Step 2: Determine the number of black male rabbits.
- Total male rabbits: 32
- White male rabbits: 14
- Thus, black male rabbits \( = 32 - 14 = 18 \)
#### Step 3: Calculate the totals for each color.
- Number of white rabbits:
- White male rabbits \( = 14 \)
- White female rabbits \( = 7 \)
- Total white rabbits \( = 14 + 7 = 21 \)
- Number of black rabbits:
- Black male rabbits \( = 18 \)
- Black female rabbits \( = 9 \)
- Total black rabbits \( = 18 + 9 = 27 \)
Now, the two-way table looks like this:
\begin{tabular}{|c|c|c|}
\hline
& Male & Female & Total \\
\hline
White & 14 & 7 & 21 \\
\hline
Black & 18 & 9 & 27 \\
\hline
Total & 32 & 16 & 48 \\
\hline
\end{tabular}
This completes part (a) of the question.
### Part b) Finding the Probability of Choosing a White Female Rabbit
To find the probability that a randomly chosen rabbit is a white female, we use the following formula for probability:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \][/tex]
In this case:
- The number of favorable outcomes (white female rabbits) \( = 7 \)
- The total number of possible outcomes (total rabbits) \( = 48 \)
Thus, the probability is:
[tex]\[ \text{Probability}(\text{white female rabbit}) = \frac{7}{48} \][/tex]
So the detailed answers to the questions are:
a) The two-way table is completed as shown.
b) The probability that a randomly chosen rabbit is a white female rabbit is [tex]\( \frac{7}{48} \approx 0.1458 \)[/tex] or about 14.58%.
