In Exercises 21-28, 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 as Mendel claimed?

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Step 1: Understand the problem. We are tasked with estimating the probability of getting a green pea based on the given data and comparing it to Mendel's expected value. The data provided includes 428 green peas and 152 yellow peas.

Step 2: Calculate the total number of peas. Add the number of green peas and yellow peas: Total peas = 428 + 152.

Step 3: Estimate the probability of getting a green pea. Use the formula for probability: P(green pea) = (Number of green peas) / (Total number of peas). Substitute the values from the problem into this formula.

Step 4: Compare the estimated probability to Mendel's expected value. Mendel's expected probability for green peas is typically 3/4 (based on Mendelian genetics for dominant traits). Check if the estimated probability is reasonably close to 3/4.

Step 5: Interpret the result. Discuss whether the estimated probability aligns with Mendel's claim and consider any potential reasons for discrepancies, such as sample size or experimental error.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it is calculated by dividing the number of favorable outcomes (green peas) by the total number of outcomes (green and yellow peas combined). Understanding probability is essential for estimating the chances of obtaining a green pea from the given sample.

Expected Value

The expected value is a theoretical average of all possible outcomes of a random variable, weighted by their probabilities. In Mendelian genetics, the expected ratio of green to yellow peas can be derived from Mendel's laws of inheritance. Comparing the calculated probability of green peas to the expected value helps assess the validity of Mendel's claims regarding inheritance patterns.

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations, based on the principles established by Gregor Mendel. His experiments with pea plants led to the formulation of laws of segregation and independent assortment, which predict the distribution of traits. Understanding these principles is crucial for interpreting the results of Mendel's experiments and the probabilities associated with different phenotypes.

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In Exercises 21-28, find the probability and answer the questions.

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