Coin flips. If you flip a fair coin 10 times, what is the probability of
(a) getting all tails?
(b) getting all heads?
(c) getting at least one tails?
Dice rolls. If you roll a pair of fair dice, what is the probability of
(a) getting a sum of 1?
(b) getting a sum of 5?
(c) getting a sum of 12?
Swing voters. A Pew Research survey asked 2,373 randomly sampled registered voters their political affiliation (Republican, Democrat, or Independent) and whether or not they identify as swing voters. 35% of respondents identified as Independent, 23% identified as swing voters, and 11% identified as both.21
(a) Are being Independent and being a swing voter disjoint, i.e. mutually exclusive?
(b) Draw a Venn diagram summarizing the variables and their associated probabilities.
(c) What percent of voters are Independent but not swing voters?
(d) What percent of voters are Independent or swing voters?
(e) What percent of voters are neither Independent nor swing voters?
(f) Is the event that someone is a swing voter independent of the event that someone is a political Indepen- dent?