Probability: Probability is used to determine the chance of an outcome occurring in any one trial. It is equal to the expected proportion of an outcome in a series of events. Example: Outcome: X-bearing or Y-bearing sperm Events: All sperm in an ejaculate Trial: Fertilization of a single egg Probability: 1/2 for X, 1/2 for Y

• Law of Independence: Applies if the occurrence of an outcome in one trial does not influence the probability of another outcome in a subsequent trial. Example: Given that a couple has had one boy, the probability that their next offspring is male is still 1/2.

• Multiplication Rule: The combined probability of two or more independent outcomes happening in two or more trials is the product of their individual probabilities. [a and b - multiply] Example: The probability of a couple having two boys in row is 1/2 x 1/2 = 1/4. • Addition Rule: The probability of two or more alternative outcomes happening in the same trial is the sum of their individual probabilities. [a or b - add] Example: The probability of a couple having either or boy or a girl is 1/2 + 1/2 = 1.

Waardenburg syndrome is an autosomal dominant condition that accounts for 1.4 percent of congenitally deaf persons. Given that a woman has Waardenburg syndrome (and is assumed to be a heterozygote) and a man is unaffected, what is the probability that none of their three children will be affected?

An unrelated man and woman both have a sibling affected with cystic fibrosis. The man and woman are phenotypically normal. Their parents are unaffected with CF, but are...

...analysis of Pedigree Charts
Principle: The Mendelian concept of dominance and segregation can also be studied in humans
by preparing and then analysing the pedigree charts. The internationally approved symbols for
indicating males and females, marriages, various generations (I, II, III), etc., are given below.
Requirement: Information about characters/traits in a family for more than one generation
Procedure
Select a family in which any one of the monogenic traits such as tongue
rolling, widow's peak, blood groups’, red-green colour blindness, dimple in
LABORATORY MANUAL: BIOLOGY
the cheek, hypertrichosis of ear, hitch-hiker's thumb, etc., is found. Ask the
person exhibiting the trait to tell in which of his/her parents, grand parents
(both maternal and paternal), their children and grand children the trait in
question is present. Among surviving individuals the trait may also be
examined. The information made available is the basis for the preparation of
pedigree chart using the appropriate symbols. A careful examination of the
pedigree chart would suggest whether the gene for the character is autosomelinked dominant or recessive, X - chromosome linked dominant or recessive,
Y- chromosome linked or not.
Explanation
1.
Autosome Linked Dominant traits: These are the traits whose
encoding gene is present on any one of the autosomes, and the wildtype allele is recessive to its mutant...

...Pedigree Analysis Activity
Pedigree charts are often constructed to show the inheritance of genetic conditions within a family. Such charts are a great help in determining whether a phenotype is controlled by a dominant, recessive or sex-linked allele. This activity will introduce you to autosomal pedigree charts.
Part I - Understanding the Pedigree
1. Table I shows the symbols needed in understanding apedigree. In Figure I, Generation I is made up of grandparents, Generation II is their children and Generation III is their grandchildren.
Table I - Pedigree Key Figure I - Sample Pedigree
Q1 - How many normal males are represented in Figure I? ______ Normal females? ______
Q2 - How many children did the grandparents have? ______
Q3 - How many affected individuals are present? ______
Part II - Pedigree Analysis
1. Individuals who lack an enzyme needed to form the skin pigment melanin are called albinos. Normal skin pigmentation is dominant. Use N to represent the gene for normal and nn to represent the genotype for albinism. If you cannot determine if the dominant trait is heterozygous or homozygous, use N_. Refer to Figure II and identify the genotype of each individual. Write the genotypes of each individual on the diagram.
FIGURE II - ALBINISM PEDIGREE
Q4 - How many individuals had the...

...of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the long-run average of the variable, or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is , formally defined by
Variance - The variance of a discrete random variable X measures the spread, or variability, of the distribution, and is defined by
The standard deviation is the square root of the variance.
Expectation - The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.
E(X) = S x P(X = x)
So the expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average.
2. Define the following;
a) Binomial Distribution - is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Therewith the probability of an event is defined by its binomial...

...PROBABILITY DISTRIBUTION
In the world of statistics, we are introduced to the concept of probability. On page 146 of our text, it defines probability as "a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur" (Lind, 2012). When we think about how much this concept pops up within our daily lives, we might be shocked to find the results. Oftentimes, we do not think in these terms, but imagine what the probability of us getting behind the wheel of a car twice a day, Monday through Friday, and arriving at work and home safely. Thankfully, the probability for me has been 'one'! This means that up to this point I have made it to work and returned home every day without getting into an accident. While probability might have one outcome with one set of circumstances, this does not mean it will always turn out that way. Using the same example, just because I have arrived at work every day without getting into an accident, this does not mean it will always be true. As I confess with my words, and pray it does stay the same, probability tells me there is room for a different outcome.
In business, we often look at the probability of success or financial gain when making a decision. There are several things to take into consideration such as the experiment, potential outcomes, and possible events. An...

...CHAPTER 3: PROBABILITY DISTRIBUTION
3.1
RANDOM VARIABLES AND PROBABILITY DISTRIBUTION
Random variables is a quantity resulting from an experiment that, by chance, can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable.
3.2
DISCRETE RANDOM VARIABLE
A random variable is called a discrete random variable if its set of posibble outcomes is countable. Probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. For example, the probability distribution of rolling a die once is as below: Outcome, x Probability, P(x) 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6
The probability distribution for P(x) for a discrete random variable must satisfy two properties: 1. The values for the probabilities must be from 0 to 1; 0 ≤ ( ) ≤ 1 2. The sum for P(x) must be equal to 1; ∑ ( ) = 1
QMT200
3.2.1 FINDING MEAN AND VARIANCE Mean of X is also referred to as its “expected value”.
= ( ) Where: = ∑[ ( )]
( )=
= (
) − [ ( )]
(
)=
[
( )] = ( )
Example 1 An experiment consists of tossing two coins simultaneously. Write down the sample space. If X is the number of tails observed,...

...OBJECTIVE: Construct a pedigree for a family when given genotypes or phenotypes of the family members.
TASK INSTRUCTIONS: Prepare a three-page report in which you draw and analyze the pedigree of the following family.
Subject: affected woman
Subject's two brothers, unaffected
Subject's father affected, mother unaffected
Subject's paternal aunt and uncle, unaffected
Subject's paternal grandfather affected, grandmother unaffected
In your 3-page report, present the following:
1. Introduction Introduce the problem and list the data.
2. Pedigree Chart Draw the pedigree according to the standard format.
3. Identification Identify each individual in the pedigree with a number.
4. Analysis In the Analysis section, make a section for possible modes of inheritance (autosomal dominant, autosomal recessive, X-linked dominant, X-linked recessive, Y-linked).
5. Within each section assign putative genotypes to each individual in the pedigree (you may do this by labeling a diagram or listing the individuals). State whether the mode of inheritance is possible given the pattern in the pedigree. Make any other relevant comments.
6. Conclusion State the conclusion of the analysis.
http://hihg.med.miami.edu/code/http/modules/education/Design/Print.asp?CourseNum=1&LessonNum=3
http://www.uvm.edu/~cgep/Education/Inheritance2.html...

...Chapter 1
The Problem and Its Background
Introduction
Changes are permanent thing on earth. Are the people is ready enough to accept the changes on the educational system? The current opening of classes here in the Philippines usually starts from June to March but our lawmakers want to amend the opening of classes. The existing school calendar which spans from June to March is often disrupted as destructive typhoons plague the region during the rainy season that’s why our lawmakers decided to move the opening of classes from September through May to avoid numerous class suspensions and serve to protect the students during strong typhoons. The Department of Education said that it is open to the proposal by some sectors, including lawmakers to move the opening of classes but they want to ensure the comfort of the students in school and stresses the need for a comprehensive study.
While the Department of Education is open on the proposal, some did not welcome this idea. An initial survey on the matter conducted way back in 2009. On the respondents, 66 percent were against the move while 34 percent were in favor. [1] Also, another ground for rejecting the proposal is the traditions celebrated during summer and being not conducive in learning because of hot weather during March. The delay in suspension of classes is one of the reasons why our lawmakers and other sectors in the community urge to move the classes from June to September. Unexpected suspension of classes is...

...the probability of an event?
1.5, 0, = ,0
#34 More Genetics In Problem 33, we learned that for some diseases, such as sickle-cell anemia, an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example, Huntington’s disease only requires one dominant gene for an individual to contract the disease. Suppose that a husband and wife, who both have a dominant Huntington’s disease allele (S) and a normal recessive allele (s), decide to have a child.
(a) List the possible genotypes of their offspring. (a) Sample space is {SS,Ss,sS,ss} where S=dominant disease allele and s=normal recessive allele
(b) What is the probability that the offspring will not have Huntington’s disease? In other words, what is the probability that the offspring will have genotype ss? Interpret this probability(b) Since P(S)=P(s)=1/2 and S,s are independent, P(offspring will not have Huntington’s disease)=P(SS)=P(S)*P(S)=1/4
#40. Which of the assignments of probabilities should be used if the coin is known to be fair?
If coin is fair, then assignment A is used because P(H)=P(T)=1/2
#48. Classifying Probability Determine whether the probabilities on the following page are computed using classical methods, empirical methods, or subjective methods.
a) The probability of having eight girls in an eight-child family is...

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