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Ausmumof3

Anyone care to help me get my head around this math problem!

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I don’t have much knowledge/background in statistics and this math problem is not really explained in the teachers guide!

singapore math 6B workbook pg 119

there is a table of men versus woman callers to a quiz on a radio station with 6 out of the 15 calls being men.

what is the probability that the 16th caller is male?

what is the probability that the 100th caller is female?  

I feel like I should know how to do this but I don’t and none of the problems that are demonstrated in the textbook are really similar conceptually.  

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I would still think that it should be 50% for the 16th caller and 100th caller because of unconditional probability. Kind of like a coin toss situation where given what we think is an unbiased coin, the probability of the next coin toss being a head or tail would still be 50%.

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Well there could be something influencing the caller gender like the host or topic of the quiz show so I don’t think it’s as random as a coin toss.  I would have thought the probability should be the same as the calculated experimental probability based on the first 15 callers 40pc and 60pc respectively.  But I could also accept 50pc.  However the answer guide has 43.75pc and 50pc - no idea how or why that would work!  I did find a Singapore forum and there was some discussion over there that seems to indicate the answer manual was probably wrong.

so I’m no longer stressing and thinking I need to enrol my kid in online math because I’ve no idea what I’m doing at least!  I’m trying to up my statistics knowledge with an EDX course though!

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23 minutes ago, Ausmumof3 said:

Well there could be something influencing the caller gender like the host or topic of the quiz show so I don’t think it’s as random as a coin toss.  I would have thought the probability should be the same as the calculated experimental probability based on the first 15 callers 40pc and 60pc respectively.  But I could also accept 50pc.  However the answer guide has 43.75pc and 50pc - no idea how or why that would work!  

 

There isn’t enough information provided by the question on how bias the sample is e.g. how many of the potential callers are males and how many are females, as well as total number of potential callers.

43.75 is (6+1)/(15+1)= 7/16 don’t know why they compute it that way

The 100th callers having a 50% chance could be due to 100 being a decent sample size and the probability approaches an unbiased sample probability.

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Just now, Arcadia said:

 

There isn’t enough information provided by the question on how bias the sample is e.g. how many of the potential callers are males and how many are females, as well as total number of potential callers.

43.75 is (6+1)/(15+1)= 7/16 don’t know why they compute it that way

The 100th callers having a 50% chance could be due to 100 being a decent sample size and the probability approaches an unbiased sample probability.

I wonder if the wording of the question has been edited?  Maybe originally it asked for a new calculation of the new experimental probability if the 16th caller was male instead of the calculation of the probability that the 16th caller was male.  Then the 7/16 would make sense.  

I also assume they aren’t looking for 50/50 because the previous questions are asking for the probability based on the experimental data I.e 6/15 x 100= 40pc.  These we had no issue with.  

 

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I would think 6/15 for men and (15-6)/15 for women.

Each event is independent.

It's not totally random because women may be more likely to call in or listen to this show.

But, I'm on a treadmill right now so my brain may be malfunctioning.

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