91Ó°ÊÓ

In a sample of pea offspring, 428 were green while 152 were yellow.

Theprobability of an event is the ratio of two numbers; favorable counts over total counts in the sample.

In terms of fraction, the probability of an event A can be written as follows:

$P\left(A\right)=\frac{\text{Counts of favourable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

The total number of offspring is the sum of the number of green offspring and yellow offspring. It is computed as follows:

$$\begin{gathered} \text{Total}\text{number}\text{of}\text{sample}\text{offspring}=428+152 \\ =580 \end{gathered}$$

The number of green peas is equal to 428.

Define an event G as the number of green offspring.

The probability of a green offspring is as follows:

$$\begin{gathered} P\left(G\right)=\frac{\text{Number}\text{of}\text{green}\text{offspring}}{\text{Total}\text{number}\text{of}\text{offspring}} \\ =\frac{428}{580} \\ =0.738 \end{gathered}$$

Therefore, the probability of a green offspring is equal to 0.7380.

The probability value of a green offspring as claimed by Mendel is calculated as follows:

$$\begin{gathered} \text{Expected}\text{Probability}=\frac{3}{4} \\ =0.75 \end{gathered}$$

The calculated probability (0.738) is approximately the same as the expected probability (0.75).

Thus, it can be said that the estimated probability of a green offspring is equal to the probability that Mendel claimed.