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in phenotype and genotype between an organism and its parents in a. Drosophila b. corn c. Neurospora 26. A drone (male) honeybee is haploid (arising from unfertilized eggs), and a queen (female) is diploid. Draw a testcross between a dihybrid queen and a drone. How many different kinds of sons and daughters might result from this cross 27. The plant Arabidopsis thaliana has ve pairs of chromosomes: AA, BB, CC, DD, and EE. If this plant is self-fertilized, what chromosome complement would be found in a root cell of the offspring a. A B C D E b. AA BB CC DD EE c. AAA BBB CCC DDD EEE d. AAAA BBBB CCCC DDDD EEEE 28. In wheat, the haploid number is twenty-one. How many chromosomes would you expect to nd in a. the tube nucleus b. a leaf cell c. the endosperm
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CHROMOSOMAL THEORY OF HEREDITY
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22. In corn (see g. 3.30), the diploid number is twenty. How many chromosomes would you nd in a(n) a. sporophyte leaf cell d. pollen grain b. embryo cell e. polar nucleus c. endosperm cell 23. If a dihybrid corn plant is self-fertilized, what genotypes of the triploid endosperm can result If you know the endosperm genotype, can you determine the genotype of the embryo 24. Change the generalized life cycles of gure 3.1 so they describe the life cycles of human beings, peas, and Neurospora. 25. If the cytoplasm rather than nuclear genes controlled inheritance, what might be the relationship
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29. A hypothetical organism has two distinct chromosomes (2n 4) and fty known genes, each with two alleles. If an individual is heterozygous at all known loci, how many gametes can be produced if a. all genes behave independently b. all genes are completely linked
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1. Can meiosis occur in a haploid cell can mitosis
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2. What is the minimum number of chromosomes that an organism can have the maximum number
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Suggested Readings for chapter 3 are on page B-1.
Tamarin: Principles of Genetics, Seventh Edition
II. Mendelism and the Chromosomal Theory
4. Probability and Statistics
The McGraw Hill Companies, 2001
PROBABILITY AND STATISTICS
STUDY OBJECTIVES
1. To understand the rules of probability and how they apply to genetics 71 2. To understand the use of the chi-square statistical test in genetics 74
STUDY OUTLINE
Probability 71 Types of Probabilities 71 Combining Probabilities 71 Use of Rules 72 Statistics 74 Hypothesis Testing 74 Chi-Square 76 Failing to Reject Hypotheses 77 Summary 78 Solved Problems 78 Exercises and Problems 79 Critical Thinking Questions 81
An agricultural worker studies variability in plants in a greenhouse. Probability in uences the differences among organisms. ( David Joel/Tony Stone Images.)
Tamarin: Principles of Genetics, Seventh Edition
II. Mendelism and the Chromosomal Theory
4. Probability and Statistics
The McGraw Hill Companies, 2001
Probability
n an experimental science, such as genetics, scientists make decisions about hypotheses on the basis of data gathered during experiments. Geneticists must therefore have an understanding of probability theory and statistical tests of hypotheses. Probability theory allows geneticists to construct accurate predictions of what to expect from an experiment. Statistical testing of hypotheses, particularly with the chi-square test, allows geneticists to have con dence in their interpretations of experimental data.
probability that the next child born will have phenylketonuria is 1/10,000. The odds based on the geometry of an event are, for example, like the familiar toss of dice. A die (singular of dice) has six faces. When that die is tossed, there is no reason one face should land up more often than any other. Thus, the probability of any one of the faces being up (e.g., a four) is one-sixth: P a/n 1/6
Similarly, the probability of drawing the seven of clubs from a deck of cards is P 1/52
PROBABILITY
Part of Gregor Mendel s success was due to his ability to work with simple mathematics. He was capable of turning numbers into ratios and deducing the mechanisms of inheritance from them. Taking numbers that did not exactly t a ratio and rounding them off to t lay at the heart of Mendel s deductive powers. The underlying rules that make the act of rounding to a ratio reasonable are the rules of probability. In the scienti c method, scientists make predictions, perform experiments, and gather data that they then compare with their original predictions (see chapter 1). However, even if the bases for the predictions are correct, the data almost never exactly t the predicted outcome. The problem is that we live in a world permeated by random, or stochastic, events. A bright new penny when ipped in the air twice in a row will not always give one head and one tail. In fact, that penny, if ipped one hundred times, could conceivably give one hundred heads. In a stochastic world, we can guess how often a coin should land heads up, but we cannot know for certain what the next toss will bring. We can guess how often a pea should be yellow from a given cross, but we cannot know with certainty what the next pod will contain. Thus, we need probability theory to tell us what to expect from data. This chapter closes with some thoughts on statistics, a branch of mathematics that helps us with criteria for supporting or rejecting our hypotheses.
The probability of drawing a spade from a deck of cards is P 13/52 1/4
The probability (assuming a 1:1 sex ratio, though the actual ratio is about 1.06 males per female born in the United States) of having a daughter in any given pregnancy is P 1/2
And the probability that an offspring from a self-fertilized dihybrid will show the dominant phenotype is P 9/16
From the probability formula, we can say that an event with certainty has a probability of one, and an event that is an impossibility has a probability of zero. If an event has the probability of P, all the other alternatives combined will have a probability of Q 1 P; thus P Q 1. That is, the probability of the completely dominant phenotype in the F2 of a selfed dihybrid is 9/16. The probability of any other phenotype is 7/16, and when the two are added together, they equal 16/16, or 1.
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