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Sampling

Posted on 2016-07-18
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Last Modified: 2016-07-19
Can you please tell me if this is correct?  Thanks

A selection of​ soft-drink users is asked to taste the two disguised soft drinks and indicate which they prefer. The accompanying data contains the results of a simulated challenge on a college campus.      
                                                                  
Age      Preference      Age      Preference      Age      Preference      Age      Preference      Age      Preference      Age      Preference
17      Brand B      21      Brand A      21      Brand B      19      Brand A      21      Brand A      18      Brand B
19      Brand A      16      Brand A      18      Brand B      23      Brand B      19      Brand B      22      Brand B
21      Brand A      20      Brand A      21      Brand A      24      Brand A      19      Brand A      22      Brand B
19      Brand B      19      Brand A      16      Brand A      19      Brand A      20      Brand B      21      Brand A
18      Brand A      19      Brand A      19      Brand B      21      Brand B      18      Brand A            
24      Brand B      21      Brand B      23      Brand A      20      Brand A      20      Brand B            
22      Brand A      18      Brand A      17      Brand B      22      Brand B      20      Brand A            
20      Brand A      20      Brand A      19      Brand B      21      Brand B      17      Brand B            
22      Brand B      22      Brand A      24      Brand A      22      Brand B      21      Brand B            
19      Brand B      19      Brand A      20      Brand A      21      Brand B      20      Brand A            
16      Brand A      24      Brand A      24      Brand A      22      Brand B      17      Brand B            
16      Brand A      21      Brand B      16      Brand B      18      Brand B      21      Brand A            
21      Brand B      22      Brand A      18      Brand B      22      Brand B      16      Brand A            
22      Brand B      21      Brand B      22      Brand B      20      Brand B      16      Brand A            
22      Brand B      20      Brand A      19      Brand B      19      Brand B      23      Brand B            
19      Brand B      19      Brand A      22      Brand A      19      Brand B      20      Brand B            
24      Brand B      22      Brand A      23      Brand B      23      Brand B      21      Brand A            
17      Brand A      21      Brand A      16      Brand B      22      Brand A      23      Brand A            
20      Brand B      24      Brand B      24      Brand A      21      Brand B      18      Brand B            
                                                                  
a. Determine the probability that a randomly chosen student prefers Brand A.                                                                  
                                                                  
​P(Brand ​A) = 47/114                                                                  
                                                                  
b. Determine the probability that one of the students prefers Brand A and is less than 18 years old.

P(Brand A and Age <18​) = 7/114

c. Of those students who are less than 18 years​ old, calculate the probability that a randomly chosen student      
prefers​ (1) B and A and​ (2) Brand B.                                                                  
P(Brand A if Age <18​) = 6/114
​P(Brand B if Age <18​) = 6/114

P(Brand A if Age≥18​) =  34/114
​P(Brand B if Age≥18​) =  38/114

d. Of those students who are at least 18 years​ old, calculate the probability that a randomly chosen student                        
prefers​ (1) Brand A and​ (2) Brand B.                                                                  
P(Brand A  if Age ≥18​) = 38/114
​P(Brand B if Age≥18​) = 42/114
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Question by:mustish1
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3 Comments
 
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Expert Comment

by:sdstuber
ID: 41718104
there are only 99 students in your sample data,  where are you getting 114?
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sdstuber earned 2000 total points
ID: 41718108
also, questions c and  aren't looking at the entire population, they are only looking at students less than 18.

I guess that could be a misreading of the question's intent though.
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Author Closing Comment

by:mustish1
ID: 41719246
Thanks.
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