A hen laid exactly 6 eggs each week for 3 weeks of a 12 week period. The same hen also laid 4 eggs or fewer each week for 6 weeks during the same 12 week period.

Question

Question 1
Based on the data, what is the probability that the hen will lay exactly 6 eggs next week?
Responses
A











1 4
B











1 6
C











3 4
D











3 6
Question 2
What is the chance that the hen will lay 4 eggs or fewer next week?
Responses
A 25% chance25% chance
B 40% chance40% chance
C 50% chance50% chance
D 60% chance

Answer 1

To analyze the probability of the hen's egg-laying behavior over the 12-week period, we first need to summarize the information provided regarding her egg-laying activities.

1. The hen laid 6 eggs each week for 3 weeks.
2. The hen laid 4 eggs or fewer during 6 weeks.

Let's determine the total number of weeks where the hen's egg-laying behaviors have been reported:

• Total weeks: 12
• Weeks with 6 eggs laid: 3
• Weeks with 4 eggs or fewer: 6

Since we know that some of the weeks with 4 or fewer eggs might overlap with weeks where she laid 6 eggs, we should analyze the non-overlapping behavior:

Assuming that the hen can lay either 6 eggs or 4 or fewer eggs but not simultaneously, we can conclude with the following:

• 3 weeks she laid 6 eggs.
• The maximum number of weeks left is \( 12 - 3 = 9 \).
• Of these 9 weeks, 6 weeks had 4 eggs or fewer, which means we have accounted for 6 weeks of the 9.
• This implies the remaining 3 weeks (9 - 6 = 3) must have been weeks where she laid more than 4 but less than 6 (possibly less than or equal to 5).

Given the possible scenarios, we don’t have specified data on how many eggs were laid outside of these behaviors (like laying 5 eggs). However, we can focus on what we know for the question.

Question 1: Probability of laying exactly 6 eggs next week

The total number of weeks where exactly 6 eggs were laid is 3 weeks out of 12 total weeks.

The probability of laying exactly 6 eggs next week can be represented as: \[ P(6 \text{ eggs}) = \frac{\text{Number of weeks with 6 eggs}}{\text{Total number of weeks}} = \frac{3}{12} = \frac{1}{4} \]

Thus, the answer to Question 1 is: A. \( \frac{1}{4} \)

Question 2: Chance of laying 4 eggs or fewer next week

The total number of weeks where the hen laid 4 eggs or fewer is 6 weeks out of the 12 total weeks.

Similarly, the probability of laying 4 or fewer eggs next week can be represented as: \[ P(4 \text{ eggs or fewer}) = \frac{\text{Number of weeks with 4 or fewer eggs}}{\text{Total number of weeks}} = \frac{6}{12} = \frac{1}{2} = 50% \]

Thus, the answer to Question 2 is: C. 50% chance