Question

in a genetics experiment on peas, one sample of offspring contained 430 green peas and 308 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 \\(\frac{3}{4}\\) that was expected?

the probability of getting a green pea is approximately 0.583
(type an integer or decimal rounded to three decimal places as needed.)

is this probability reasonably close to \\(\frac{3}{4}\\)? choose the correct answer below.

\\(\bigcirc\\) a. yes, it is reasonably close
\\(\bigcirc\\) b. no, it is not reasonably close

Explanation:

Part 1: Calculating the Probability of Green Peas

Step 1: Find Total Number of Peas

To find the total number of peas, we add the number of green peas and yellow peas. Let \( G = 430 \) (green peas) and \( Y = 308 \) (yellow peas). The total number of peas \( T = G + Y \).
\( T = 430 + 308 = 738 \)

Step 2: Calculate Probability of Green Peas

The probability \( P(Green) \) is the number of green peas divided by the total number of peas. So, \( P(Green) = \frac{G}{T} \).
\( P(Green) = \frac{430}{738} \approx 0.583 \) (rounded to three decimal places)

Part 2: Checking if Probability is Close to \( \frac{3}{4} \)

First, convert \( \frac{3}{4} \) to a decimal. \( \frac{3}{4} = 0.75 \). Now, compare \( 0.583 \) with \( 0.75 \). The difference between \( 0.75 \) and \( 0.583 \) is \( 0.75 - 0.583 = 0.167 \), which is a significant difference. So, \( 0.583 \) is not reasonably close to \( 0.75 \).

Answer:

s:
The probability of getting a green pea is approximately \( \boldsymbol{0.583} \).
For the second part, the correct answer is: B. No, it is not reasonably close.