Homework 05: Probability Computations
I'm having trouble with #6
Burger preferences
A 2010 SurveyUSA poll asked 491
Los Angeles residents, "What is the best hamburger place in Southern California? Five Guys Burgers? In-N-Out Burger? Fat Burger? Tommys Hamburgers? Umami Burger? Or somewhere else?" The distribution of responses by gender is shown below:
d) What is the probability that a man and a woman who are dating both like In-N-Out the best? Assuming their burger tastes are independent?
For this one I was thinking 347/491 but it is incorrect.
e) What is the probability that a randomly chosen person likes Umami best or that person is female? For this one I was thinking 2/491, but that was also incorrect.
What am I doing wrong?
Comments
It looks to me like you did this by summing the rows and dividing. Thus, you've computed the probability that any particular person likes In-N-Out Burger the best. You need to pick two people, one man and one women, find out the probability that they both like In-N-Out the best. Thus, deal with the Male column and the Female column separately using the same technique that you applied to the Total column. That should give you two numbers and you can multiply those to get your answer.
Symbolically, we're applying the rule
$$
P(M \cap W) = P(M) \times P(W),
$$
where $M$ denotes the event that a randomly chosen man likes In-N-Out the best and $W$denotes the event that a randomly chosen woman likes In-N-Out the best.
I think you've computed $P(M \cap W)$ when you want $P(M \cup W)$.