4. Conditional vs unconditional probabilities Results for the Gallup poll results below are based on telephone interviews conducted Sept. 1-17, 2021, with a random sample of 1,005 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia. For results based on the total sample of national adults, the margin of sampling error is 14 percentage points at the 95% confidence level. All reported margins of sampling error include computed design effects for weighting. Each sample of national adults includes a minimum quota of 70% cellphone respondents and 30% landline respondents, with additional minimum quotas by time zone within region. Landline and cellular telephone numbers are selected using random-digit-dial methods. a) "Eight months after President Joe Biden's inauguration, his job approval rating has fallen six percentage points to 43%, the lowest of his presidency. For the first time, a majority, 53%, now disapproves of Biden's performance." i i) Is the 43% approval rating above a conditional or unconditional probability? State what the population or subpopulation is to support your answer. ii) Is the 53% disapproval rating above a conditional or unconditional probability? State what the population or subpopulation is to support your answer. iii) Do the approval and disapproval probabilities add up to 100%? If so, explain why they should. If not, explain why they might not. b) "Democrats' approval of the job Biden is doing has remained high and not varied by more than eight points since he took office. ... their lowest [rating] is the current 90%." Is the 90% approval rating above a conditional or unconditional probability? State what the population or subpopulation is to support your answer. c) "Republicans' ratings of Biden are similarly stable at the other extreme, ranging from 12% in February and July to 6% this month." Is the 6% current approval rating above a conditional or unconditional probability? State what the population or subpopulation is to support your answer. d) "Independents have shown the greatest variation in their opinions of how Biden is doing. Biden's current 37% approval rating among independents is his lowest to date ..." Is the 37% current approval rating above a conditional or unconditional probability? State what the population or subpopulation is to support your answer. e) "For the first time, Gallup asked Americans to evaluate how Vice President Kamala Harris is doing in her role. Her ratings are better than Biden's by six points, with 49% approving and 49% disapproving." Is the 49% current approval rating above a conditional or unconditional probability? State what the population or subpopulation is to support your answer. Is the 49% current disapproval rating above a conditional or unconditional probability? State what the population or subpopulation is to support your answer. Should the two probabilities above sum to 100%? Explain why or why not