Scientist Gregor Mendel (1822-1884) is often called the "father of modern genetics" and is famous for his work involvingthe inheritance of certain traits in pea plants. Suppose that the genes controlling the color of peas are Y for yellow and yfor green. Each plant has two genes, one from the female (seed) and one from the male (pollen). The Y gene is dominant,and therefore a plant with genes YY will have yellow peas, a plant with genes Yy or yY will have yellow peas, and a plantwith genes yy will have green peas.If a plant with two yellow genes (YY) is crossed with a plant with two green genes (yy), the result is four hybrid offspringwith genotypes Yy. The offspring will be yellow, but will carry the recessive green gene.Parent 2УYy YyYy YyyParent 1Suppose that both parent pea plants are hybrids with genotype Yy.a. Make a chart showing the possible genotypes of the offspring.b. What is the probability that a given offspring will have green peas?c. What is the probability that a given offspring will have yellow peas?Parent 2yParent 1У

a) Chart for possible genotypes of the offspring. Y y Y YY Yy y Yy yy

Answered: Scientist Gregor Mendel (1822-1884) is…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 12 cars, chosen at random. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 11 12 Brand 1 0.64 0.53 0.32 0.61 0.59 0.64 0.34 0.58 0.53 0.43 0.38 0.34 Brand 2 0.47 0.48 0.31 0.37 0.56 0.37 0.30 0.57 0.49 0.41 0.50 0.17 Difference(Brand 1 - Brand 2) 0.17…
Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment. An experiment is conducted to compare peach-tree seedling growth when the soil and weeds are treated with one of two herbicides. In a field containing 20 seedlings, 10 are randomly selected throughout the field and assigned to receive Herbicide A. The remainder of the seedlings is assigned to receive Herbicide B. Soil and weeds for each seedling are treated with the appropriate herbicide, and at the end of the study period the height in centimeters is recorded for each seedling. The following results are obtained: Mean Std. Dev. Herbicide A 94.5 cm 10 cm Herbicide B 109.1 cm 9 cm Reference: Ref 7-14 Suppose we wish to determine if there tends to be a difference in height for the seedlings treated with the different herbicides. Find the P-value for this test assuming the standard deviations of the two populations are equal.
Example 2.9 Suppose that a particular trait of a person (such as eye color or left handedness) is classified on the basis of one pair of genes and suppose that d represents a dominant gene and r a recessive gene. Thus a person with dd genes is pure dominance, one with rr is pure recessive, and one with rd is hybrid. The pure dominance and the hybrid are alike in appearance. Chil- dren receive one gene from each parent. If, with respect to a particular trait, two hybrid parents have a total of four children, what is the probability that exactly three of the four children have the outward appearance of the dominant gene?
One urn, U1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn, U2, contains two red balls (labeled R4 and R5) and two blue balls (labeled B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. (a) Which of the following is a possibility tree that shows all possible outcomes of this experiment?
At a certain genetic locus on a chromosome, each individual has one of three different DNA sequences (alleles). The three alleles are denoted A, B, C. At another genetic locus on the same chromosome, each organism has one of three alleles, denoted 1, 2, 3. Each individual therefore has one of nine possible allele pairs: A1, A2, A3, B1, B2, B3, C1, C2, or C3. These allele pairs are called haplorypes. The loci are said to be in linkage equilibrium if the two alleles in an individual's haplotype are independent. Haplotypes were determined for 316 individuals. The following MINITAB output presents the results of a chi-square test for independence. Chi-Square Test: A, B, C Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts в с Total 66 44 34 144 61.06 47.39 35.54 0.399 0.243 0.067 2 36 38 20 94 39.86 30.94 23.20 0.374 1.613 0.442 3 32 22 24 78 33.08 25.67 19.25 0.035 0.525 1.170 Total 134 104 78 316 Chi-Sq = 4.868, DF = 4, P-Value =…
A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 8 cars, chosen at random. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. 1 2 3 4 5 6 7 Car Brand 1 0.58 0.61 0.46 0.43 0.51 0.62 0.62 0.50 Brand 2 0.42 0.55 0.30 0.46 0.44 0.32 0.54 0.53 Difference 0.16 0.06 0.16 -0.03 0.07 0.30 0.08 -0.03 (Brand 1 - Brand 2) Send data to calculator Based on these data, can the consumer group conclude, at the 0.10 level of significance, that the mean tread wears of the brands differ? Answer this question by…
A biologist is examining two genetic mutations. Genetic mutation A occurs in 15% of the population, mutation B occurs in 4% of the population, and 1% of the population have mutation B and do not have mutation A. a) Is having mutation A independent of having mutation B? Explain/show the reasoning for your answer. b) Is not having mutation A independent of having mutation B? Explain/show the reasoning for your work.
Suppose a birth defect has a recessive form of inheritance.In a study population, the recessive gene (a) initially has aprevalence of 25%. A subject has the birth defect if bothmaternal and paternal genes are of type a. A further study finds that after 10 generations (≈200 years)a lot of inbreeding has taken place in the population. Twosubpopulations (populations A and B), consisting of 30%and 70% of the general population, respectively, haveformed. Within population A, prevalence of the recessivegene is 40%, whereas in population B it is 10%. Suppose that a baby is born with a birth defect,but the baby’s ancestry is unknown. What is the posteriorprobability that the baby will have both parents from population A, both parents from population B, or mixed ancestry,respectively? (Hint: Use Bayes’ rule.)
A supermarket buys light globes (light bulbs) from three different manufacturers –Brightlight (35%), Glowglobe (20%) and Shinewell (45%). In the past, the supermarket has found that 1% of Brightlight’s globes are faulty and that 1.5% of each of Glowglobe’s and Shinewell’s globes are faulty. A customer buys a globe without looking at the manufacturer’s name –in other words, it’s a random choice. When she gets home, she finds the globe is faulty. What is the probability she chose a Shinewell’s globe?
A survey was conducted in 1990 asking American high school students to name their favorite subject inschool. This survey found that, in 1990, the following proportions of students named each subject astheir favorite: 30% History, 25% Math, 20% English, 15% Biology, 10% Chemistry. A researcher in theyear 2020 conducts an identical survey, in order to see if students’ favorite subjects have shifted overthe 30 years that have passed since the 1990 study was done. The researcher gives the survey to n=60high school students, and gets the following observed frequencies and expected frequencies. FREQUENCY History Math English Biology Chemistry TOTAL fo 20 18 10 5 7 60 fe (.30)(60) = (.25)(60) = (.20)(60) = (.15)(60) = (.10)(60) = 18 15 12 9 6 60 What is the χ2critical that you…
A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same 10 cars, chosen at random. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 Brand 1 0.46 0.59 0.48 0.62 0.40 0.42 0.59 0.54 0.42 0.42 Brand 2 0.32 0.41 0.37 0.43 0.24 0.49 0.51 0.44 0.44 0.44 0.14 Difference (Brand 1- Brand 2) 0.18 0.10 0.11 0.19 0.16 -0.07 0.08 -0.02 -0.02 Send data to calculator V Based on these data, can the consumer group conclude, at the 0.05 level of significance, that the mean tread wears of the…

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