Lecture 5: Probability
1. Distinguish between the following pairs in a manner that makes it clear that you know what each is and how they differ.
a. Mutually exclusive events and independent events.2. What is wrong with the following statement? The probability of receiving an A grade in any class is about 0.2. Therefore the probability of any student receiving A grades in 5 classes in one semester is about (0.2)5 = 0.00032.
b. Product rule and sum rule.
c. Conditional probability and combined probabilities.
d. Ordered probability and unordered probability.
e. p and q (as used in binomial calculations in genetics)
f. p and q (as used to describe the arms of chromosomes).
3. In throwing dice, what are the probabilities of the following: (Caution: do not use formulas that are inappropriate for the number of alternatives that you are working with.)
a. Two dice both showing 1.4. In Drosophila, Lobe eyes is dominant and ebony body is recessive. These genes undergo independent assortment and are not sex-linked. Parents that are heterozygous for both loci are mated. Ten of their progeny are selected at random without examining sex or phenotypic properties. What is the probability of obtaining exactly six females with Lobed eyes and ebony bodies. (Hint, remember that p is the ordered probability of obtaining the combination you are seeking and q=1-p).
b. Two dice showing a 1 and a 6.
c. In six throws obtaining each of the six possible numbers once.
d. Obtaining the numbers 1, 2, 3, 4, 5, 6 in that sequence.
e. Obtaining the same number six times in a row. .
5. You are doing a monohybrid F2 phenotypic distribution in which you expect a 3:1 ratio. What is the probability that you will obtain exactly 48 dominant phenotypes if you examine 64 F2 individuals? (Don't try this one without a scientific calculator that can handle numbers up to 10100. If you do not have such a calculator, just set up the equation with the numbers.)
6. Galactosemia is an autosomal recessive trait. A couple who are phenotypically normal (for galactosemia) have an affected child. Determine the probability that:
a. the next three children will all be unaffected.7. Describe the circumstances under which you would employ each of the following:.
b. the next two children will both be galactosemic.
c. of the next four children, one and only one will be galactosemic.
d. the father of the galactosemic child is heterozygous for galactosemia.
e. the next child born to the couple will be heterozygous.
f. that an unaffected older brother of the galactosemic child is heterozygous.
g. that the next child will be a girl and galactosemic.
a. binomial probability8. Why is it not possible to use the binomial theorem to calculate probabilities related to throwing dice, as in problem 3 above?
b. forked line method.
c. product rule
d.. sum rule
e. conditional probability
f. ordered probability
g. unordered probability
9. Two plants that are heterozygous at six unlinked genetic loci are crossed. What is the probability of obtaining progeny that exhibit three dominant phenotypes and three recessive phenotypes.
10. A plant that is heterozygous at six unlinked genetic loci is test crossed. What is the probability of obtaining progeny that exhibit three dominant phenotypes and three recessive phenotypes?
11. A family has five children whose birth order has been boy, girl, boy, girl, boy. What is the probability that a sixth child will be a girl?
12. What is the probability of the first five children being born in the sequence described in question 11?
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