Question

In Exercises 25–32, find the probability and answer the questions. Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the expected value of 3/4, as Mendel claimed?

Short answer

The probability of the offspring being a green pea is equal to 0.7380.

Yes, the probability value obtained is approximately equal to the claimed value $\frac{3}{4}$.

Step-by-step solution

Given information

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

Probability

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:

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

Calculating the probability value

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.

Comparison with expected value

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.