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. Question 3 a) List the sample space for presidential candidates running in the Iowa Democratic caucus from the table below. Democratic Presidential Candidate mammm- m m