Here you will be required to write a report about a random experiment. This can be anything ranging from testing viruses and etc. (100 points)

Before rolling a die you do not know the result. This is an example of a random experiment. In particular, a random experiment is a process by which we observe something uncertain. After the experiment, the result of the random experiment is known. An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set. Here are some examples of random experiments and their sample spaces:

Random experiment: toss a coin; sample space: S={heads,tails} or as we usually write it, {H,T}.

Random experiment: roll a die; sample space: S={1,2,3,4,5,6}.

Random experiment: observe the number of iPhones sold by an Apple store in Boston in 2015; sample space: S={0,1,2,3,⋯}.

Random experiment: observe the number of goals in a soccer match; sample space: S={0,1,2,3,⋯}.

When we repeat a random experiment several times, we call each one of them a trial. Thus, a trial is a particular performance of a random experiment. In the example of tossing a coin, each trial will result in either heads or tails. Note that the sample space is defined based on how you define your random experiment. For example,

Example  

We toss a coin three times and observe the sequence of heads/tails. The sample space here may be defined as

S={(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),(T,T,T)}.

Our goal is to assign probability to certain events. For example, suppose that we would like to know the probability that the outcome of rolling a fair die is an even number. In this case, our event is the set E={2,4,6}. If the result of our random experiment belongs to the set E, we say that the event E has occurred. Thus an event is a collection of possible outcomes. In other words, an event is a subset of the sample space to which we assign a probability. Although we have not yet discussed how to find the probability of an event, you might be able to guess that the probability of {2,4,6} is 50 percent which is the same as 12 in the probability theory convention.

Outcome: A result of a random experiment.

Sample Space: The set of all possible outcomes.

Event: A subset of the sample space.

Union and Intersection: If A and B are events, then A∪B and A∩B are also events. By remembering the definition of union and intersection, we observe that A∪B occurs if A or B occur. Similarly, A∩B occurs if both A and B occur. Similarly, if A1,A2,⋯,An are events, then the event A1∪A2∪A3⋯∪An occurs if at least one of A1,A2,⋯,An occurs. The event A1∩A2∩A3⋯∩An occurs if all of A1,A2,⋯,An occur. It can be helpful to remember that the key words "or" and "at least" correspond to unions and the key words "and" and "all of" correspond to intersections.

an individual’s sex (i.e., whether they are a male or female) is determined by the sex chromosomes. most people have two sex chromosomes, one that is inherited from their mother and one that is inherited from their father. typically, females have two x chromosomes (xx) and males have one x chromosome and one y chromosome (xy). conditions caused by changes (“mutations”) in genes located on the x chromosome are considered x-linked.

x-linked recessive inheritance

most x-linked conditions are recessive. this means that in a person with two x chromosomes (most females), both copies of a gene (i.e., one on each x chromosome) must have a change or mutation whereas in a person with one x chromosome (most males), only one copy of a gene must have a mutation. a female with a mutation in one copy of a gene on the x chromosome is said to be a “carrier” for an x-linked condition. a male with a mutation in a gene on the x chromosome is typically affected with the condition. because females have two copies of the x chromosome and males have only one x chromosome, x-linked recessive diseases are more common among males than females. however, x-linked recessive diseases can occur in both males and females.

for x-linked recessive disorders, an unaffected carrier mother who has a mutation in a gene on the x chromosome can transmit either the x chromosome with this mutation or a “normal” x chromosome to her children. if the father is unaffected, none of her daughters will be affected and all of her daughters will be unaffected—since they will inherit at least one normal x chromosome from their father. however, each daughter will have a 50% chance of being an unaffected carrier like her mother and a 50% chance of both x chromosomes being normal.

c. the initial amount of money placed in the savings account