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Question 1135875: 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.
(please round any numerical answers to 4 decimal places)
Male Female Total
Five Guys Burgers 5 6 11
In-N-Out Burger 162 181 343
Fat Burger 10 12 22
Tommy's Hamburgers 27 27 54
Umami Burger 5 1 6
Other 26 20 46
Not Sure 13 5 18
Total 248 252 500
a) Are being female and liking Five Guys Burgers mutually exclusive?
Explain:
b)What is the probability that a randomly chosen male likes In-N-Out the best?
Incorrect
c) What is the probability that a randomly chosen female likes In-N-Out the best?
Incorrect
d) What is the probability that a man and woman who are dating like In-N-Out the best?
Incorrect
What assumptions did you need to make? Are those assumptions reasonable?
Incorrect
e) What is the probability that a randomly chosen person likes Umami best or that person is female?
Incorrect
here's a screenshot of the problem with the table: https://prnt.sc/msbfhq
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Part A
The events are not mutually exclusive because there are 6 females who like Five Guys Burgers best. If these two events were mutually exclusive, then this value would be 0. Mutually exclusive events are two such events where they cannot happen at the same time.
An example of mutual exclusive events would be the events "heads" and "tails" on some coin. You can only have one event happen, but not both at the same time.
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Part B
Focus only on the male column. We have 248 total and 162 who like In-N-Out Burger best, so the probability is therefore,
162/248 = 0.65322580645161 = 0.6532
It appears you have the right idea but you only put the answer accurate to two decimal places (rather than four).
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Part C
This time we only focus on the female column
181 females like In-N-Out Burger best
252 females total
181/252 = 0.71825396825397 = 0.7183
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Part D
Define the two events
M = event that a male likes In-N-Out Burger best
N = event that a female likes In-N-Out Burger best
From the previous parts (B and C), we found that
P(M) = probability male likes In-N-Out best
P(M) = 0.6532
and
P(N) = probability female likes In-N-Out best
P(N) = 0.7183
Assuming the events M and N are independent, this would allow us to multiply the probability values
P(M and N) = P(M)*P(N)
P(M and N) = 0.6532*0.7183
P(M and N) = 0.46919356
P(M and N) = 0.4692
The key thing is that the formula only works if M and N are independent. Each person surveyed is likely to not worry about what other people are doing or thinking, since they are probably alone taking it. So no single person affects any other in terms of whether they like a certain burger place. Also, a person's tastes are unique to them so even if others are present, they aren't likely to sway an opinion. The survey has a subjective base to it (ie there is no right or wrong answer).
So in short, the assumption needed to be made is that the events are independent. It's is reasonable to assume this.
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Part E
252 females
6 people like Umami Burger best
1 person is both female and they like Umami Burger best
252+6-1 = 257 people are either female, like Umami Burger best, or both apply
note: you subtract off that 1 person because they are in both categories, so effectively this one person is counted twice when we added the 252 and 6 together
There are 257 people we want out of 500 total, so the probability is:
257/500= 0.5140
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