Student Number: 23 TA: Tongji Section: 097 Homework 02 Version 1.8, February 2019 Written by Derek Gordon Genetics Lab 382 In this program, you will be asked to solve 10 problems. You will find the problems in the file with your assigned student number and TA in the name of the file. Please make sure you perform this homework. Here we go! The problems here are related to conditional probabilities. For each of the alien species provided, individuals are humanoid in their genetics. You will be asked two types of problems: TYPE I - SMALL SAMPLE (i ) For a small sample, compute probabilities that a random individual has a given trait phenotype, or a pair of phenotypes (note, gender is a phenotype); and (ii) for the same sample, compute conditional probabilities. TYPE II - LARGE SAMPLE (POPULATION) The types of questions will be the same as above (i) and (ii), only you will be give proportions instead of integer counts. You will be able to figure out the type of problem from the information provided in the question. HERE WE GO!! Problem 1. Among Romulans, there is a trait known as Reas Romulus Betta; Romulans with this trait enjoy watching Romulan Fish produce flourescent skin colors. Those who don't have Reas Romulus Betta do not watch these fish. You are performing a study with a large population of subjects. The proportions of individuals with phenotype-pairs is as follows: The proportion of individuals who are male and have Reas Romulus Betta is 0.155; The proportion of individuals who are female and have Reas Romulus Betta is 0.448; The proportion of individuals who are male and do not have Reas Romulus Betta is 0.107; The proportion of individuals who are female and do not have Reas Romulus Betta is 0.29. Question A. What is the probability a Romulan is female in this population? Question B. What is the probability a Romulan has Reas Romulus Betta and is female? Question C. What is the probability a Romulan has Reas Romulus Betta given that she is female? Problem 2. Among Romulans, there is a trait known as Reas Romulus Betta; Romulans with this trait enjoy watching Romulan Fish produce flourescent skin colors. Those who don't have Reas Romulus Betta do not watch these fish. You are performing a study with a large population of subjects. The proportions of individuals with phenotype-pairs is as follows: The proportion of individuals who are male and have Reas Romulus Betta is 0.0321; The proportion of individuals who are female and have Reas Romulus Betta is 0.241; The proportion of individuals who are male and do not have Reas Romulus Betta is 0.369; The proportion of individuals who are female and do not have Reas Romulus Betta is 0.357. Question A. What is the probability a Romulan is female in this population? Question B. What is the probability a Romulan does not have Reas Romulus Betta and is female? Question C. What is the probability a Romulan does not have Reas Romulus Betta given that she is female? Problem 3. Among Vulcans, there is a trait known as Sehlat Fangus Magma; Vulcans with this trait enjoy petting large Sehlats. Note that Sehlats are like live Teddy Bears with fangs. Those who don't have Sehlat Fangus Magma prefer petting small Sehlats. As a research geneticist, you perform a study with a sample size of 68 subjects. The breakdown of individuals by phenotypes is as follows: 12 individuals are male and have Sehlat Fangus Magma; 17 individuals are female and have Sehlat Fangus Magma; 22 individuals are male and do not have Sehlat Fangus Magma; 17 individuals are female and do not have Sehlat Fangus Magma. Question A. What is the probability a Vulcan does not have Sehlat Fangus Magma? Question B. What is the probability a Vulcan does not have Sehlat Fangus Magma and is male? Question C. What is the probability a Vulcan is male given that he does not have Sehlat Fangus Magma? Problem 4. Among Vulcans, there is a trait known as Sehlat Fangus Magma; Vulcans with this trait enjoy petting large Sehlats. Note that Sehlats are like live Teddy Bears with fangs. Those who don't have Sehlat Fangus Magma prefer petting small Sehlats. As a research geneticist, you perform a study with a sample size of 54 subjects. The breakdown of individuals by phenotypes is as follows: 14 individuals are male and have Sehlat Fangus Magma; 10 individuals are female and have Sehlat Fangus Magma; 9 individuals are male and do not have Sehlat Fangus Magma; 21 individuals are female and do not have Sehlat Fangus Magma. Question A. What is the probability a Vulcan has Sehlat Fangus Magma? Question B. What is the probability a Vulcan has Sehlat Fangus Magma and is female? Question C. What is the probability a Vulcan is female given that she has Sehlat Fangus Magma? Problem 5. Among Romulans, there is a trait known as Reas Romulus Betta; Romulans with this trait enjoy watching Romulan Fish produce flourescent skin colors. Those who don't have Reas Romulus Betta do not watch these fish. You are performing a study with a large population of subjects. The proportions of individuals with phenotype-pairs is as follows: The proportion of individuals who are male and have Reas Romulus Betta is 0.291; The proportion of individuals who are female and have Reas Romulus Betta is 0.271; The proportion of individuals who are male and do not have Reas Romulus Betta is 0.221; The proportion of individuals who are female and do not have Reas Romulus Betta is 0.217. Question A. What is the probability a Romulan is female in this population? Question B. What is the probability a Romulan does not have Reas Romulus Betta and is female? Question C. What is the probability a Romulan does not have Reas Romulus Betta given that she is female? Problem 6. Among Vulcans, there is a trait known as Sehlat Fangus Magma; Vulcans with this trait enjoy petting large Sehlats. Note that Sehlats are like live Teddy Bears with fangs. Those who don't have Sehlat Fangus Magma prefer petting small Sehlats. As a research geneticist, you perform a study with a sample size of 69 subjects. The breakdown of individuals by phenotypes is as follows: 25 individuals are male and have Sehlat Fangus Magma; 23 individuals are female and have Sehlat Fangus Magma; 10 individuals are male and do not have Sehlat Fangus Magma; 11 individuals are female and do not have Sehlat Fangus Magma. Question A. What is the probability a Vulcan has Sehlat Fangus Magma? Question B. What is the probability a Vulcan has Sehlat Fangus Magma and is female? Question C. What is the probability a Vulcan is female given that she has Sehlat Fangus Magma? Problem 7. Among Romulans, there is a trait known as Reas Romulus Betta; Romulans with this trait enjoy watching Romulan Fish produce flourescent skin colors. Those who don't have Reas Romulus Betta do not watch these fish. You are performing a study with a large population of subjects. The proportions of individuals with phenotype-pairs is as follows: The proportion of individuals who are male and have Reas Romulus Betta is 0.199; The proportion of individuals who are female and have Reas Romulus Betta is 0.288; The proportion of individuals who are male and do not have Reas Romulus Betta is 0.395; The proportion of individuals who are female and do not have Reas Romulus Betta is 0.118. Question A. What is the probability a Romulan is female in this population? Question B. What is the probability a Romulan has Reas Romulus Betta and is female? Question C. What is the probability a Romulan has Reas Romulus Betta given that she is female? Problem 8. Among Romulans, there is a trait known as Reas Romulus Betta; Romulans with this trait enjoy watching Romulan Fish produce flourescent skin colors. Those who don't have Reas Romulus Betta do not watch these fish. You are performing a study with a large population of subjects. The proportions of individuals with phenotype-pairs is as follows: The proportion of individuals who are male and have Reas Romulus Betta is 0.302; The proportion of individuals who are female and have Reas Romulus Betta is 0.306; The proportion of individuals who are male and do not have Reas Romulus Betta is 0.362; The proportion of individuals who are female and do not have Reas Romulus Betta is 0.0302. Question A. What is the probability a Romulan is female in this population? Question B. What is the probability a Romulan does not have Reas Romulus Betta and is female? Question C. What is the probability a Romulan does not have Reas Romulus Betta given that she is female? Problem 9. Among Vulcans, there is a trait known as Sehlat Fangus Magma; Vulcans with this trait enjoy petting large Sehlats. Note that Sehlats are like live Teddy Bears with fangs. Those who don't have Sehlat Fangus Magma prefer petting small Sehlats. As a research geneticist, you perform a study with a sample size of 59 subjects. The breakdown of individuals by phenotypes is as follows: 6 individuals are male and have Sehlat Fangus Magma; 11 individuals are female and have Sehlat Fangus Magma; 17 individuals are male and do not have Sehlat Fangus Magma; 25 individuals are female and do not have Sehlat Fangus Magma. Question A. What is the probability a Vulcan is male? Question B. What is the probability a Vulcan has Sehlat Fangus Magma and is male? Question C. What is the probability a Vulcan has Sehlat Fangus Magma given that he is male? Problem 10. Among Romulans, there is a trait known as Reas Romulus Betta; Romulans with this trait enjoy watching Romulan Fish produce flourescent skin colors. Those who don't have Reas Romulus Betta do not watch these fish. You are performing a study with a large population of subjects. The proportions of individuals with phenotype-pairs is as follows: The proportion of individuals who are male and have Reas Romulus Betta is 0.292; The proportion of individuals who are female and have Reas Romulus Betta is 0.318; The proportion of individuals who are male and do not have Reas Romulus Betta is 0.359; The proportion of individuals who are female and do not have Reas Romulus Betta is 0.0308. Question A. What is the probability a Romulan is female in this population? Question B. What is the probability a Romulan does not have Reas Romulus Betta and is female? Question C. What is the probability a Romulan does not have Reas Romulus Betta given that she is female?