2.5

If you flip a fair coin 10 times, what is the probability of…
a) Getting all tails? .5^10 = .0009765625
b) Getting all heads? .5^10 = .0009765625
c) Getting at least one tails? 1-.0009765625 = 0.9990234375

2.7

  1. Are being Independent and being a swing voter disjoint, i.e. mutually exclusive? No

  2. Draw a Venn diagram summarizing the variables and their associated probabilities.

  3. What percent of voters are Independent but not swing voters? 24%
  4. What percent of voters are Independent or swing voters? 47%
  5. What percent of voters are neither Independent nor swing voters? 53%

  6. Is the event that someone is a swing voter independent of the event that someone is a political Independent? No

2.19

  1. Are being female and liking Five Guys Burgers mutually exclusive?
    No

  2. What is the probability that a randomly chosen male likes In-N-Out the best?
    162/248 = .65
  3. What is the probability that a randomly chosen female likes In-N-Out the best?
    181/252 = .72
  4. What is the probability that a man and a woman who are dating both like In-N-Out the best? Note any assumption you make and evaluate whether you think that assumption is reasonable.
    Assumption is that the event of a man and woman who are dating each liking In-N-Out is independent of each other: (162/248) x (181/252) = .47

  5. What is the probability that a randomly chosen person likes Umami best or that person is female?
    (6/500) + (252/500) = .52

2.29

  1. Suppose you draw a chip and it is blue. If drawing without replacement, what is the probability the next is also blue? 2/9=.22
  2. Suppose you draw a chip and it is orange, and then you draw a second chip without replacement. What is the probability this second chip is blue? 3/9=.33
  3. If drawing without replacement, what is the probability of drawing two blue chips in a row? (3/10) x (2/9) = .0667
  4. When drawing without replacement, are the draws independent? Explain. They are dependant because each subsequent draw is from a reduced pool overall and and a reduced number of any specific color(s) drawn previously

2.43

  1. What fraction of these cats weigh less than 2.5 kg?
sum(cats$Bwt < 2.5)/nrow(cats)
## [1] 0.3541667
  1. What fraction of these cats weigh between 2.5 and 2.75 kg?
sum(cats$Bwt >=2.5 & cats$Bwt <= 2.75)/nrow(cats)
## [1] 0.2152778
  1. What fraction of these cats weigh between 2.75 and 3.5 kg?
sum(cats$Bwt >=2.75 & cats$Bwt <= 3.5)/nrow(cats)
## [1] 0.3680556