Questions: In a genetics experiment on peas, one sample of offspring contained 432 green peas and 34 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 3/4 that was expected? The probability of getting a green pea is approximately 0.927. (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to 3/4 ? Choose the correct answer below. A. No, it is not reasonably close. B. Yes, it is reasonably close.

Solution Steps

In the genetics experiment, the number of green peas is \( 432 \) and the number of yellow peas is \( 34 \). The total number of peas is:

\[ \text{Total Peas} = 432 + 34 = 466 \]

The probability \( P \) of getting a green pea is calculated as follows:

\[ P(\text{Green}) = \frac{\text{Number of Green Peas}}{\text{Total Peas}} = \frac{432}{466} \approx 0.927 \]

The expected probability of getting a green pea is \( \frac{3}{4} \). We calculate the difference between the observed probability and the expected probability:

\[ \text{Expected Probability} = \frac{3}{4} = 0.75 \]

The difference \( D \) is given by:

\[ D = |P(\text{Green}) - \text{Expected Probability}| = |0.927 - 0.75| \approx 0.177 \]

To determine if the observed probability is reasonably close to the expected probability, we can set a threshold. A common threshold for "reasonably close" is \( 0.05 \).

Since:

\[ D \approx 0.177 > 0.05 \]

we conclude that the observed probability is not reasonably close to the expected probability.

Final Answer