In a genetics experiment on​ peas, one sample of offspring contained 366 green peas and 533 yellow peas. Based on those​ results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of three fourths
3
4 that was​ expected?
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Part 1
The probability of getting a green pea is approximately enter your response here.
​(Type an integer or decimal rounded to three decimal places as​ needed.)

To estimate the probability of getting a green pea, we use the **empirical probability formula**:

\[
P(\text{green pea}) = \frac{\text{Number of green peas}}{\text{Total number of peas}}
\]

Given:
- Number of green peas = 366
- Number of yellow peas = 533
- Total number of peas = \(366 + 533 = 899\)

### Step 1: Calculate the empirical probability

\[
P(\text{green pea}) = \frac{366}{899} \approx 0.407
\]

So, the probability of getting a green pea is approximately **0.407**.

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### Step 2: Compare with the expected value \( \frac{3}{4} = 0.75 \)

Clearly, the result \(0.407\) is not very close to the expected value of **0.75**. This suggests that either there might be some experimental deviation, or the underlying assumptions about the expected proportion may not hold.

---

Do you need further clarification on how these probabilities work or any other details?

Here are 5 related questions to consider:  
1. How can we interpret probabilities using relative frequency in the long term?  
2. What statistical tests can determine if the observed ratio significantly differs from the expected ratio?  
3. What could be some reasons for deviation from expected genetic outcomes?  
4. How would the probability change if the sample size was larger?  
5. How is a chi-square test used to compare observed and expected outcomes in genetics?

**Tip:** When comparing observed and expected outcomes, increasing the sample size tends to reduce random deviations.

In a genetics experiment on peas, one sample of offspring contained 366 green peas and 533 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of three fourths (3/4) that was expected?

In this genetics experiment, learn how to estimate the empirical probability of getting a green pea when the offspring sample contains 366 green peas and 533 yellow peas. Compare the observed probability of 0.407 with the expected probability of 0.75. Suitable for Grades 9-12.

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