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Subject: "Probability"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #733
Reading Topic #733
MikeS
guest
Jul-05-10, 12:19 PM (EST)
 
"Probability"
 
   A radio station asks for a caller of a specific year to call. Then the station then spins a "month" wheel for the caller to win a prize if their birth month matches the month spun up (the station does not know the birth month of the caller). Then the station spins a second "date" wheel (1 - 31) and if the caller's birth date matches the wheel (again the station does not know the birth date of the caller) they win the major prize. Assuming that the wheels have equal sections for each possibility, what are the odds of the month matching, and then the caller winning the major prize??I thin I need to apply independent rules for both wheels since the station only specifies the year, and there's 1/12 options for the caller's month and 1/12 options for the wheel... etc.


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  Subject     Author     Message Date     ID  
  RE: Probability alexbadmin Jul-05-10 1
     RE: Probability MikeS Jul-05-10 2
         RE: Probability alexbadmin Jul-06-10 3
             RE: Probability MikeS Jul-06-10 4
                 RE: Probability alexbadmin Jul-08-10 5
                     RE: Probability Kenneth Ramsey Jul-11-10 7
     RE: Probability Kenneth Ramsey Jul-09-10 6
         RE: Probability alexbadmin Jul-11-10 8

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alexbadmin
Charter Member
2532 posts
Jul-05-10, 12:29 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
1. "RE: Probability"
In response to message #0
 
   The probaility of the month matching is unquestionably 1/12. You are right about that. The answer to the question of winning the grand prize depends on how much detail you are willing (or expected) to take into account. The two wheel spins generate independent events. If all months had 31 day, the answer would be 1/12×1/31. However, the 12 months have different number of days. So people born in different month will have different probabilties of getting the grand prize.


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MikeS
guest
Jul-05-10, 00:00 AM (EST)
 
2. "RE: Probability"
In response to message #1
 
   Thanks alexb.

Since the radio station does not specify a month for the caller's birth date I was approaching the problem with the view of independent events for the caller and the wheel spin, e.g. spinning 2 wheels with 12 months each on them for the same result on each wheel.

There are 12 possibilities for the random caller's birth month, and there are 12 possibilities for the wheel to land on... 1/12 x 1/12 = 1/144 for matching months. Is this wrong? If not, then the same principle would seem to apply to the date wheel as well...

Looking forward to your replies :)


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alexbadmin
Charter Member
2532 posts
Jul-06-10, 00:10 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
3. "RE: Probability"
In response to message #2
 
   Every one has been born on a certain month. So has a specific caller. The only thing that matters is whether his/her month of birth matches the one picked up by the wheel. This means that the probability of matching a month is 1/12.

Think of something simpler. You may hold in your hand either a white or a black ball. The radio station manager picks randomly one of two colors. Regardless of which ball you are holding, the probability of a match is 1/2. This is true even if you do not know the color of your ball. It does not matter which ball is in your hand. It will be matched with the probability of 1/2.


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MikeS
guest
Jul-06-10, 10:48 AM (EST)
 
4. "RE: Probability"
In response to message #3
 
   Many thanks Alexb. I think that has cleared up my confusion.

Cheers.


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alexbadmin
Charter Member
2532 posts
Jul-08-10, 11:40 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
5. "RE: Probability"
In response to message #4
 
   It has occured to me that there is a circumstance in which your view of the problem might be justified.

This is when the wheel is spun before a call has been made. The caller is then declared a winner if his/her month of birth matches the one that the wheel shows. In this case the probability of the match is indeed 1/12×1/12.


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Kenneth Ramsey
guest
Jul-11-10, 07:43 PM (EST)
 
7. "RE: Probability"
In response to message #5
 
   I read this reply over again and I still say that the probability of a match is 1/12 * 1/31 The caller's Birth date is not variable. Also, for the month there are 12 possible matches 1<>1,2<>2,...12<>12; so 12/144 = 1/12. Same way for the day of the month there are 31 possible matches. Since the caller's birth date can be considered fixed, the only issue is whether the spin of the wheels will match the birth date. As there are only 372 possible wheel combinations and one and only one matches the caller's birthdate then the answer should be 1/372.


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Kenneth Ramsey
guest
Jul-09-10, 06:58 AM (EST)
 
6. "RE: Probability"
In response to message #1
 
   I am not sure but isn't it true that since only callers with their birthday in the year selected by the radio station would call, equate that probability to 1. Since the number of days on the day wheel is 31 and the number of months on the month wheel is 12, the probability that a caller would have his or her birth date match the radio selection would be 1* 1/12 * 1/31 regardless of the caller's birth month.


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alexbadmin
Charter Member
2532 posts
Jul-11-10, 07:50 PM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
8. "RE: Probability"
In response to message #6
 
   Disregarding the fact the the months have different number of days, the probability of matching a birthday is 1/12×1/31. There is no question about that.

The point of concern was about the probability of matching the month of birth.


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