2.19- Burger preferences. A 2010 SurveyUSA poll asked 500 Los Angeles residents, “What is the best hamburger place in Southern California? Five Guys Burgers? In-N-Out Burger? Fat Burger? Tommy’s Hamburgers? Umami Burger? Or somewhere else?” The distribution of responses by gender is shown below.

knitr::include_graphics("table.png")

  1. Are being female and liking Five Guys Burgers mutually exclusive?

    No, we can observe we have 6 women that likes Five Guys Burgers.

  2. What is the probability that a randomly chosen male likes In-N-Out the best?

    P( In-N-Out | Male)

    P = 162/248 = 0.65 = 65%

  3. What is the probability that a randomly chosen female likes In-N-Out the best?

    P( In-N-Out | Female)

    P = 181/252= 0.72 = 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.

    I made the assumntion they are disjoint/ mutually exclusive variables.
    0.72 X 0.65 = 0.468 = 46.8 %

  5. What is the probability that a randomly chosen person likes Umami best or that person is female?

    P(likes Umami or Female)

    P(A U B) = P(A) + P(B) - P(A and B)

    6 + 252 - 1
    0.012 + 0.504 - 0.002 = 0.514 = 51.4 %