Question

in a genetics experiment on peas, one sample of offspring contained 410 green peas and 329 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 0.555
(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.
a. yes, it is reasonably close.
b. no, it is not reasonably close.

Explanation:

Step1: Calculate the total number of peas

The total number of peas is the sum of green peas and yellow peas. So, \(410 + 329=739\).

Step2: Calculate the probability of getting a green pea

The probability \(P\) of an event is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (green peas) is \(410\) and the total number of outcomes is \(739\). So, \(P=\frac{410}{739}\approx0.555\).

Step3: Compare the calculated probability with \(\frac{3}{4}\)

We know that \(\frac{3}{4}=0.75\). The difference between \(0.75\) and \(0.555\) is \(|0.75 - 0.555|=0.195\). A reasonable closeness would imply a small difference. Since \(0.195\) is not a small difference (for example, if we consider a tolerance of say \(0.1\) in many basic probability - comparison scenarios), we can say it's not close.

Answer:

B. No, it is not reasonably close.