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Chapter 4: Problem 27

Find the probability and answer the questions. 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

Expert verified
The probability of a pea being green is approximately 0.737. This is reasonably close to Mendel's expected value of 0.75.

Step by step solution

01

- Calculate the Total Number of Peas

Add the number of green peas and yellow peas to find the total number of peas. Total number of peas = 428 (green peas) + 152 (yellow peas)
02

- Compute Total

Perform the addition: 428 + 152 = 580
03

- Calculate the Probability of Green Peas

Divide the number of green peas by the total number of peas to determine the probability. Probability that a pea is green = \(\frac{428}{580}\)
04

- Simplify the Probability

Simplify the fraction \(\frac{428}{580}\) to get the probability in decimal form. \(\frac{428}{580} \ = 0.737\)
05

- Compare with Mendel's Expected Probability

Compare the calculated probability (0.737) to Mendel's expected probability of \(\frac{3}{4}\), which is 0.75. Is 0.737 reasonably close to 0.75?

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mendelian Genetics
Mendelian Genetics is the foundation of understanding how traits are inherited. Mendel discovered that certain traits follow particular patterns when passed from parents to offspring. He used pea plants for his experiments and focused on the inheritance of traits like color. This laid the groundwork for what we now refer to as Mendelian inheritance, where traits are determined by pairs of genes. Each parent contributes one gene for each trait. For example, with peas, green color might be dominant, while yellow is recessive. The combination of these genes determines the pea's color.
Probability Estimation
Calculating probabilities in genetics helps us predict how often certain traits will appear in offspring. For example, in Mendel's experiment with peas, he counted 428 green peas and 152 yellow peas. To find the probability of green peas, you first calculate the total number of peas: 428 (green) + 152 (yellow) = 580. Then, you divide the number of green peas by the total number of peas: \(\frac{428}{580} \). After simplifying, you get approximately 0.737. This calculation tells us that there's about a 73.7% chance an offspring pea will be green. Next, we compare this to Mendel's theoretical prediction of 75%.
Comparative Analysis
When comparing the calculated probability (0.737) to Mendel's expected probability (0.75), it's essential to determine if they are reasonably close. Although 0.737 is slightly less than 0.75, the difference is minor. Minor differences can occur due to natural variation in experiments. This means that while Mendel's prediction was slightly off in this specific sample, it closely matches the observed results. Comparing theoretical expectations and actual outcomes helps validate theories and understand the role of chance in genetics. It shows that while Mendel's laws provide a strong predictive framework, real-world outcomes can slightly vary.

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Most popular questions from this chapter

Express all probabilities as fractions. A presidential candidate plans to begin her campaign by visiting the capitals of 5 of the 50 states. If the five capitals are randomly selected without replacement, what is the probability that the route is Sacramento, Albany, Juneau, Hartford, and Bismarck, in that order?

Let \(A=\) the event of getting at least one defective iPhone when 3 iPhones are randomly selected with replacement from a batch. Write a statement describing event \(\bar{A}\).

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Answer the given questions that involve odds. A roulette wheel has 38 slots. One slot is 0 , another is 00 , and the others are numbered 1 through 36 , respectively. You place a bet that the outcome is an odd number. a. What is your probability of winning? b. What are the actual odds against winning? c. When you bet that the outcome is an odd number, the payoff odds are \(1: 1\). How much profit do you make if you bet \(\$ 18\) and win? d. How much profit would you make on the \(\$ 18\) bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? (Recommendation: Don't actually try to convince any casino of this; their sense of humor is remarkably absent when it comes to things of this sort.)
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