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Frequency Tables: Mastery Test

Select the correct answer from the drop-down menu.

A classroom monitors chicken eggs at various temperatures. The table shows the class's recorded results. Using the data, calculate probabilities related to a randomly selected egg.

\begin{tabular}{|c|c|c|c|c|}
\hline & Cool & \begin{tabular}{l}
Room \\
Temperature
\end{tabular} & Warm & Total \\
\hline Hatched & 5 & 16 & 21 & 42 \\
\hline Unhatched & 18 & 10 & 4 & 32 \\
\hline Total & 23 & 26 & 25 & 74 \\
\hline
\end{tabular}

Based on the information, which statement about the eggs is correct?

A. Given the egg has hatched, the egg was kept warmer than room temperature.

B. Given the egg has hatched, the egg was kept at room temperature.

C. Given the egg has not hatched, the egg was kept cooler than room temperature.

D. Given the egg has not hatched, the egg was kept warmer than room temperature.



Answer :

GinnyAnswer
Let's examine the given data closely.

The table provides the following information:

```plaintext
| | Cool | Room Temperature | Warm | Total |
|----------------|------|------------------|------|-------|
| Hatched | 5 | 16 | 21 | 42 |
| Unhatched | 18 | 10 | 4 | 32 |
| Total | 23 | 26 | 25 | 74 |
```

We are interested in the probability that an egg was kept in warmer than room temperature given that it hatched. To solve this, we focus on the hatched row:

- Hatched eggs kept in cool temperature: 5
- Hatched eggs kept at room temperature: 16
- Hatched eggs kept in warm temperature: 21

The total number of hatched eggs is 42. To find the probability that a hatched egg was kept in warmer than room temperature, we'll consider only the hatched eggs that were kept in warm temperature.

Therefore, the number of hatched eggs kept in warm temperature (21) over the total number of hatched eggs (42) gives us the probability:

[tex]\[ \text{Probability} = \frac{\text{Hatched eggs in warm temperature}}{\text{Total hatched eggs}} = \frac{21}{42} = 0.5 \][/tex]

Thus, the correct statement is:

Given the egg has hatched, the probability that the egg was kept warmer than room temperature is 0.5.

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