Probability+and+Inheritance+Lab

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Dec 6, 2023

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Name: _____________________________ Date: ___________________ Probability and Inheritance Lab Background In 1866, Gregor Mendel published the results of his study of garden pea plants. Although Mendel did not fully understand the mechanisms of inheritance, his work became the basics of modern genetics. From his studies on the inheritance of traits in pea plants, Mendel formulated three laws of inheritance: the law of dominance , the law of segregation , and the law of independent assortment . Mendel thought that every trait was controlled by a pair of factors called genes . The law of dominance states that the dominant gene prevents the appearance of the trait controlled by the other gene. The law of segregation states that during gamete (egg and sperm) formation, the pair of genes separate so that each gamete has only one of the genes for the trait. The law of independent assortment states that as gametes are being formed, the genes for various traits separate independently of one another. In this activity, you will learn about the basic principles of probability. You will use these principles and Mendel’s laws to predict the inheritance of traits. Objectives In this activity you will: 1. Predict the probability of the occurrence of a single event. 2. Predict the probability of two independent events occurring at the same time. 3. Apply Mendel’s laws to predict the occurrence of certain traits in the offspring of parents exhibiting certain traits. Materials • 2 coins of the same denomination (penny, nickel, dime, or quarter) • Tape or stickers

Procedures and Observations Part 1 Occurrence of a Single Event (30 points) The law of probability states that when a procedure can result in two equally likely outcomes (heads or tails), the probability of either outcome occurring is ½ or 50%. 1. Using the law of probability, predict how many times out of 20 tosses you would expect heads to appear and how many times you would expect tails to appear. Record your answers in the Expected column for 20 tosses. 2. Toss a coin 20 times. Count and record how many times the coin lands heads up and how many times it lands tails up. 3. Calculate the deviation by subtracting the expected number from the observed number. Record the calculation in the Deviation column for 20 tosses. 4. Repeat steps 1-3, but toss the coin 30 times. 5. Repeat steps 1-3, but toss the coin 50 times. Data Table 1: Probability of the Occurrence of a Single Event Tosses Calculations Heads Tails 20 Expected 20 Observed 20 Deviation Tosses Calculations Heads Tails 30 Expected 30 Observed 30 Deviation Tosses Calculations Heads Tails 50 Expected 50 Observed 50 Deviation

Part 2 Independent Events Occurring Simultaneously (30 points) According to the law of probability, where there are four equally likely outcomes, the probability that one of the outcomes will occur is 25%. For example, we know that when tossing two coins, the probability of heads occurring on each coin is ½. The probability of heads occurring on one and tails on the other coin is also ½ for each. Therefore, the probability of heads occurring on both coins in one toss is: ½ X ½ = ¼. 1. Using the law of probability, predict the expected outcomes of tossing two coins. 2. Toss two coins simultaneously 40 times. Count and record how many times the coins land on: heads/heads, tails/heads, heads/tails, or tails/tails in the Observed column in data table 2. 3. Calculate the percent of the total that each combination occurred and record it in the percent column in data table 2. (*To calculate percent, divide each observed number by 40 and multiply by 100.) 4. Calculate the deviation by subtracting the expected number from the observed number. Record the calculation in the Deviation column. Data Table 2: Probability of Independent Events Occurring Simultaneously Combinations Expected Observed % Deviation Heads/Heads Heads/Tails Tails/Heads Tails/Tails Total 40 40 100%

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Part 3 Probability and Mendelian Genetics (20 points) We can use the law of probability to predict the probability of given genetic traits appearing in the offspring of parents. Punnett squares can also be used to make these predictions. When gametes are formed, the pair of genes that determine a particular trait separate, and one gene goes to each gamete. When fertilization occurs, a male and a female gamete fuse. The resulting zygote now contains two genes for the trait, one from each parent. Which two genes appear is the result of chance. In this case we will use the inheritance of round and wrinkled genes in pea plants. R will represent the dominant gene for round peas and r will represent the recessive gene for wrinkled peas. 1. Place a small piece of tape or a sticker on each side of two coins. On one coin write R on each side. On the other coin write r on each side. 2. Toss the coins 5 times. a. What combination of genes always appears? b. Would the offspring with these genes be round or wrinkled? 3. Replace the old tape with new tape. One each coin, write R on one side and r on the other side. Toss the coins simultaneously until all possible combination of genes have appeared. a. What combinations of genes appear? b. For each of the combinations, would the offspring be round or wrinkled?

Analysis and Conclusions (20 points) – Answer in complete sentences. 1. In Part 1, what was the expected ratio of heads to tails for tosses of a single coin? Did your results always agree with the expected ratio? If not, what would be a reason for the deviation? (4 points) 2. Compare the deviations from the expected for 20, 30, and 50 tosses. What is the relationship between the sample size and deviation? (4 points) 3. In Part 2, what was the probability that tails would appear on both coins? Explain. (4 points) 4. What was the probability that heads/tails or tails/heads would appear? Show your calculations. (Hint: The probabilities for these two combinations must be added together because they were recorded together.) (4 points) 5. If you tossed two coins simultaneously 400 times, would you expect the deviation to be greater or less than it was in tossing them 40 times? Explain. (4 points)

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