Let's break down the problem step by step using the provided data.
The table shows the distribution of eggs in different temperature conditions and whether they hatched or not. Our task is to find the probability of a certain condition given the egg has hatched.
First, note the total number of hatched eggs:
[tex]\[ \text{Total Hatched} = 42 \][/tex]
The number of hatched eggs for each temperature condition is:
- Warm: 21
- Room Temperature: 16
- Cool: 5
The probabilities we seek are:
1. Probability that a hatched egg was kept in a warm condition:
[tex]\[ P(\text{Warm}|\text{Hatched}) = \frac{\text{Number of Warm Hatched}}{\text{Total Hatched}} = \frac{21}{42} = 0.5 \][/tex]
2. Probability that a hatched egg was kept in room temperature:
[tex]\[ P(\text{Room Temperature}|\text{Hatched}) = \frac{\text{Number of Room Temperature Hatched}}{\text{Total Hatched}} = \frac{16}{42} \approx 0.38 \][/tex]
From the above probabilities, we can conclude that:
Given the egg has hatched, the probability that it was kept in a warm environment is higher (0.5) compared to it being kept at room temperature (approximately 0.38).
Hence, based on this information, the statement:
"Given the egg has [tex]$\square$[/tex] , the egg was kept warmer than room temperature."
The correct answer for the blank (filled with "hatched") is:
[tex]\[ \text{hatched} \][/tex]
So, the answer is:
Given the egg has hatched, the egg was kept warmer than room temperature.
