How to figure out solving this statistics assignment

STAT 3011, Fall 2021 b) The table above was based on an entrance poll of 1,660 democratic delegates to the Iowa caucus. Delegates were asked their presidential preference, gender, family income, political position, rst time voting, etc. before entering the caucus venue. The table represents a cross classication of presidential candidate by region. Let event R represent a delegate who is from a rural region. Let B be the event that a delegate supports Bernie Sanders. c) Calculate P(R). d) What does the event RC mean in words? Calculate P(RC). e) Find the probability that a delegate was from a rural region and supported Bernie Sanders. f) Find the probability that a delegate was from a rural region, or supported Bernie Sanders or both. g) Calculate P(RC U B). h) Are events R and B disjoint? Why or why not? Question 4 Ted Cruz won the Republican Iowa caucus by about 28% of the vote. It is believed that he won this caucus by a strong evangelical vote. About 15% of the Republican voters self identied with being evangelical. The probability that a delegate supported Ted Cruz given that they are evangelical is 80%. Let C be the event that a delegate supports Ted Cruz. Let E be the event that a delegate is evangelical Let EC be the event that a delegate is not evangelical. a) Find P(C H E). b) Statistically show using a formula whether events C and E are independent or not. c) Find P(C 0 EC). d) Find the probability that a delegate does not selfidentify with being evangelical given that they support Ted Cruz. STAT 3011, Fall 2021 Question 5 You toss two fair dice simultaneously. How many outcomes are in this sample space? Note 7 you do NOT need to list the outcomes, only report the total number of outcomes. a) Let A be the event that you roll \"Snake Eyes\STAT 3011 Homework 2 : Question 1 A single random digit is selected using software or a random number table. a) State the sample space for the possible outcomes. b) State the probability for each possible outcome, based on what you know about the way random numbers are generated. c) Each outcome in a sample space must have probability between 0 and 1, and the total of the probabilities must equal 1. Show that your assignment of probabilities in part b satises this rule. Question 2 For a family with two children, let A denote {rst child is female}, let B denote {at least one child is female}, and let C denote {both children are female}. a) Show that P(ClA) = 1/2. b) Are A and C independent events? Why or why not? c) Find P(O|B). d) Describe what makes P( , ) different than P(C|B). Question 3 a) List the sample space for presidential candidates running in the Iowa Democratic caucus from the table below. Democratic Presidential Candidate mammumm- WW Total 828 823 9 196660