To solve these questions, we first need to analyze the data regarding the hen's egg-laying behavior over the 12-week period.
Analyzing the Data
-
Laying 6 Eggs:
- The hen laid exactly 6 eggs for 3 weeks.
-
Laying 4 Eggs or Fewer:
- The hen laid 4 eggs or fewer for 6 weeks.
Now we need to determine how many weeks the hen laid a different number of eggs.
- Total weeks = 12
- Weeks laying 6 eggs = 3
- Weeks laying 4 or fewer eggs = 6
Assuming the weeks where she didn’t lay 6 eggs or 4 or fewer eggs were likely different weeks, we can infer:
- Weeks laid different amounts = 12 - (3 + 6) = 3 weeks, where the hen could have laid some other number of eggs (greater than 4 and not equal to 6).
Question 1: Probability of laying exactly 6 eggs next week
We know that:
- Total observations (weeks) = 12
- Weeks with exactly 6 eggs = 3
- Therefore, the probability of laying exactly 6 eggs next week is calculated as follows:
\[ P(6 \text{ eggs}) = \frac{\text{Number of weeks laying 6 eggs}}{\text{Total weeks}} = \frac{3}{12} = \frac{1}{4} \]
So the answer is A: 1/4.
Question 2: Probability of laying 4 eggs or fewer next week
We know that:
- Total observations (weeks) = 12
- Weeks with 4 eggs or fewer = 6
- Therefore, the probability of laying 4 eggs or fewer next week is calculated as follows:
\[ P(4 \text{ eggs or fewer}) = \frac{\text{Number of weeks laying 4 or fewer eggs}}{\text{Total weeks}} = \frac{6}{12} = \frac{1}{2} = 50% \]
So the answer is C: 50% chance.
Final Answers
- Question 1: A (1/4)
- Question 2: C (50% chance)