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Probability Distribution

Posted on 2016-07-19
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Can you please tell me if my calculations are correct?  Thanks.

a. Determine the probability that a randomly chosen student prefers Brand A.
​P(Brand ​A) = 49

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                                                                  
                                                                  
c. Of those students who are less than 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​) =      7                                                            
​P(Brand B if Age <18​) =      5                                                            
                                                                  
P(Brand A if Age≥18​) =            42                                                      
​P(Brand B if Age≥18​) =            42                                                      
                                                                  
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​) =      42                                                            
​P(Brand B if Age≥18​) =            42                                                      

Sno      Age      Preference            Sno      Age      Preference
1      16      Brand A            1      16      Brand B
2      16      Brand A            2      16      Brand B
3      16      Brand A            3      17      Brand B
4      16      Brand A            4      17      Brand B
5      16      Brand A            5      17      Brand B
6      16      Brand A            6      18      Brand B
7      17      Brand A            7      18      Brand B
8      18      Brand A            8      18      Brand B
9      18      Brand A            9      18      Brand B
10      18      Brand A            10      19      Brand B
11      19      Brand A            11      19      Brand B
12      19      Brand A            12      19      Brand B
13      19      Brand A            13      19      Brand B
14      19      Brand A            14      19      Brand B
15      19      Brand A            15      19      Brand B
16      19      Brand A            16      19      Brand B
17      19      Brand A            17      19      Brand B
18      19      Brand A            18      19      Brand B
19      20      Brand A            19      20      Brand B
20      20      Brand A            20      20      Brand B
21      20      Brand A            21      20      Brand B
22      20      Brand A            22      20      Brand B
23      20      Brand A            23      20      Brand B
24      20      Brand A            24      21      Brand B
25      20      Brand A            25      21      Brand B
26      20      Brand A            26      21      Brand B
27      20      Brand A            27      21      Brand B
28      21      Brand A            28      21      Brand B
29      21      Brand A            29      21      Brand B
30      21      Brand A            30      21      Brand B
31      21      Brand A            31      21      Brand B
32      21      Brand A            32      21      Brand B
33      21      Brand A            33      21      Brand B
34      21      Brand A            34      22      Brand B
35      21      Brand A            35      22      Brand B
36      22      Brand A            36      22      Brand B
37      22      Brand A            37      22      Brand B
38      22      Brand A            38      22      Brand B
39      22      Brand A            39      22      Brand B
40      22      Brand A            40      22      Brand B
41      22      Brand A            41      22      Brand B
42      23      Brand A            42      22      Brand B
43      23      Brand A            43      23      Brand B
44      24      Brand A            44      23      Brand B
45      24      Brand A            45      23      Brand B
46      24      Brand A            46      23      Brand B
47      24      Brand A            47      24      Brand B
48      24      Brand A            48      24      Brand B
49      24      Brand A            49      24      Brand B
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Question by:mustish1
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LVL 73

Expert Comment

by:sdstuber
ID: 41719595
probabilities are a quotient (x/y) that range in value from 0 to 1

therefore, without even looking at your math
 all of your results should be immediately obvious as incorrect.

you could alternatively report them as percentages which then implies a 100 divisor.
0
 

Author Comment

by:mustish1
ID: 41719604
I just count them based on the equation. I dont know how to i shows them in 1 and 0 form.

P(Brand A if Age <18​) =      7                                                            
​P(Brand B if Age <18​) =      5                                                            
                                                                 
P(Brand A if Age≥18​) =            42                                                      
​P(Brand B if Age≥18​) =            42
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LVL 73

Accepted Solution

by:
sdstuber earned 500 total points
ID: 41719631
a probability means an event happens  x  times out of y trials.

like 2 out of 3  (2/3 or 0.66667)  ,  5 out of 10  (5/10 or 0.5), etc.

if 7 is the count of something, then 7 out of what?  the total population  (98)?
if so, that's fine, but that needs to be included.

So, not 7  but 7/98
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Author Closing Comment

by:mustish1
ID: 41719686
Thanks.
0
 

Author Comment

by:mustish1
ID: 41719692
I MA NOT SURE IF  THIS IS CORRECT?

P(Brand A if Age≥18​) =            42  / 49                                                    
​P(Brand B if Age≥18​) =            42  / 49                                                    
                                                                 
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​) =      42  /98                                                        
​P(Brand B if Age≥18​) =        42   / 98
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