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ntitative Literacy Hannah Thompson 03/20/25 9:31 PM Question 10, 11.4.26 HW Score: \( 78.33 \%, 7.83 \) of 10 points Part 5 of 5 Points: 0 of 1 Save A pea plant must have exactly one of each of the following pairs of traits: short (s) or tall ( \( t \) ), round \( (r) \) or wrinkled \( (w) \) seeds, and white (wh) or purple (p) flowers (for example, short, round with white flowers). Complete parts a) through d). Use the fundamental counting principle to determine the answer to part a). Assume that each event is equally likely to occur. (b) Use a tree diagram to determine all the classifications possible. Choose the correct tree diagram below. Click here to view diagram d. Click here to view diagram b. Click here to view diagram c . Click here to view diagram a. Determine all the classifications possible. Choose the correct answer below. A. SRWh, SRP, SWWh, SWP, TRWh, TRP B. SRWh, SRP, SWWh, SWP C. SRWh, SRP, SWWh, SWP, TRWh, TRP, TWWh, TWP D. SRWh, TWP (c) If each characteristic is equally likely, find the probability that the pea plant will have round seeds. The probability is \( \frac{1}{2} \). (Simplify your answer.) (d) If each characteristic is equally likely, determine the probability that the pea plant will be short, have wrinkled seeds, and have purple flowers.

Ask by Pearson Ortiz. in the United States
Mar 21,2025

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Answer

There are 8 possible classifications: SRWh, SRP, SWWh, SWP, TRWh, TRP, TWWh, TWP. The probability of having round seeds is 1/2, and the probability of being short, having wrinkled seeds, and purple flowers is 1/8.

Solution

1. There are three pairs of traits. For each pair there are 2 options, so by the fundamental counting principle there are \[ 2 \times 2 \times 2 = 8 \] classifications possible. 2. The tree diagram for these classifications must show 8 outcomes. The correct set of outcomes is: \[ \text{SRWh},\; \text{SRP},\; \text{SWWh},\; \text{SWP},\; \text{TRWh},\; \text{TRP},\; \text{TWWh},\; \text{TWP} \] This corresponds to option C. 3. Each characteristic is equally likely. Since there are 2 seed types, the probability that the pea plant will have round seeds is \[ \frac{1}{2}. \] 4. The probability of obtaining one specific classification (short, wrinkled seeds, and purple flowers) among 8 equally likely outcomes is \[ \frac{1}{8}. \]

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The Deep Dive

Pea plants are part of the rich legacy of Mendelian genetics, pioneered by Gregor Mendel in the 19th century. Mendel's experiments with pea plants allowed him to develop the foundational principles of heredity, such as dominance and segregation. His work initially went unnoticed, but today it’s celebrated as the cornerstone of modern genetics, showcasing how traits are passed from one generation to the next, like the delightful variety of pea plants' traits that you’re working on! In the real-world application of genetics, understanding the different traits and how they combine can help in agricultural practices, such as breeding new plant varieties with desired characteristics. This not only enhances crop yield but also improves resilience to diseases. So, whether you're creating the next champion pea plant in your backyard or developing sustainable agricultural practices on a larger scale, using concepts like the fundamental counting principle and tree diagrams is essential to predict genetic outcomes!

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