Introduction-
Probability is the measure of the likeliness that an event will occur.
Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. The aim of this investigation is to solve a long-standing probability question; The Monty Hall problem. I chose this topic for a number of reasons. Firstly, we have just started studying probability in class and I enjoy learning and working ahead.
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An example of a conditional probability question would be as follows;
Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?
While the obvious answer is ½ this is not true. Let us look at the possibilities possible:
Case 1- boy and boy
Case 2- boy and girl
Case 3- girl and boy
Case 4- girl and girl
As the problem states that Mr. Smith has 2 children one of whom is a boy, we case safely remove case 4. Hence the probability of both Mr. Smith’s children being boys is;
=(case 1)/(# of cases )
=1/3
The Monty Hall Problem-
The Monty Hall Problem’s origin is from the TV show, “Let’s Make A Deal” hosted by Monty Hall. The statement of the problem is as follows: “You are a contestant in a game show in which a prize is hidden behind one of three curtains. You will win the prize if you select the correct curtain. After you have picked one curtain but before the curtain is lifted, the emcee lifts one of the other curtains, revealing an empty stage, and asks if you would like to switch from your current selection to the remaining curtain. How will your chances change if you
1. Suppose two Dd birds mate. What percentages of DD, Dd, and dd offspring would you predict? Use the Punnett square at right to help determine your answer.
For partial credit, formulas and work, appropriately labeled, must be shown. There is no partial credit for multiple choice or true/false questions.
Pascal’s Wager has been argued to be impractical because our beliefs are often not in our control. This argument is
9. No, because each child's 2 sets of chromosomes are rearranged independently, so that there is an equal probability of all of them having the same genotype (1/2^4, or 1/16) as there is of them having all different ones
2. Indicate on your pedigree chart the individuals who are carriers by shading half of each circle or square.
Based on your results for the female offspring, predict whether color blindness is a dominant or recessive trait. Explain your reasoning.
• The family consists of the mother and two children. The mother is forty-five years old, the son is 20, and the daughter is 18.
In a family with two children, what are the chances that both children are girls?
The lottery is one of the oldest known game of chance, dating all the way back to 205 B.C. in the Han Dynasty. Being built upon pure luck, it has garnered attention all over the world in it's various forms of existence. After money began its association with the lottery in l443, it became even more popular worldwide. While existing in multiple forms, the most popular form of lottery is the randomly selected number method, where winnings are based on the correct numbers predicted. It is estimated that nearly half of the citizens living in the United States have participated in the lettery. An alarmingly high number ef the participants have admitted to lottery as their only chance ef being financially secure. what exactly are the edde of winnieg the Lottery? new is the probability te win increased? ?his mathematical inveetigatien hepes to shed light on these queries.
Swift breaks down the number of children born per year. He calculated that of the 120,000 poor children, 20,000 should be reserved for breeding purposes and ¼ of that amount should be males. So one male can serve four female breeders. The rest of the 100,000 can be offered for sale at one
You are also provided with a heterozygous female, and a homozygous recessive male for a genetic cross. In this particular female, all the dominant alleles are on one chromosome, and the recessive counterparts are on the other homologous chromosome. Due to a chromosomal condition, in the female no recombination occurs between the M and N loci. Normal recombination occurs between the L and M loci. Diagram this cross, and show the genotypes and frequencies of all offspring expected from this cross.
This is different than today’s society because today gardening is shared among males and females and we know that it is actually the males X or Y chromosome that determine the sex of a child.
While both short stories can be considered entertaining, W. W. Jacobs’ “The Monkey’s Paw” does an overall better job at using characterization, irony and foreshadowing to create the long-lasting effect of suspense. Throughout the story, Jacobs creates a theme which can be interpreted in many ways such as: “Be careful what you wish for.” or “Evil can come in the most unexpected forms,“ (such as the paw). If the theme of evil and regret is present before the story is even introduced, the reader is automatically pulled into this preconceived idea that there will be a great amount of suspense. This idea continues to be confirmed as the story develops.
Boys are two times more likely than girls to receive such a diagnosis. (King, 2013).
The participants were three members of a family. The first was male and 67 years of age. The second was female and 52 years old. The third member of the family was male, and 25 years old.