beacohen97 Posted April 14, 2015 Report Share Posted April 14, 2015 (Sorry this is so long but really need urgent help! Draft due next week!) Hi everyone, So I've been stuck on my Maths IA for a while after having to change topics because my old one was too fiddly. I've discussed doing the Birthday Paradox with my teacher, and she said it was a good topic. However, I'm on holidays now and have sent her an email asking about a problem I was having and possible solutions. In her reply she said she was worried I wasn't doing enough maths. What I was previously planning on doing in the IA was: - Discussing the Birthday Paradox itself and the maths behind it (how many people do you need to have in a group so that there is an over 50% probability of 2 people sharing the same birthday - the answer is 23) - Using the maths of the paradox to calculate how many people you would need for that probability to be 70%, and then 90% - Investigate whether this works in real life by getting a random sample of 100 of my Facebook friends, and then randomly selecting the number needed for 70% and 90% probabilities and seeing whether it matches up (eg. if the answer for 70% was 30, I would do 10 random selections of 30 of the 100 Facebook friends and see whether 7 out of 10 trials had at least 2 people sharing a birthday) However, the problem I came across was to do with calculating the number needed for 70% and 90%. Most websites discuss the paradox by using the already known answer for 50% (23) and proving it using a relatively simple calculation. In order to find the number 23 itself, you need to use the Poisson approximation, which my teacher previously said would be too complicated. I thought that maybe I could get around this either:a) by selecting a number of people and finding the probability from there (although it would make it more complicated to investigate in terms of real life as it is unlikely it would be a round number like 70%) or b) Using a pre-made graph (which is reliable as the results appear the same on many different websites) of the probabilities from 0% to >99% to estimate the number of people needed for 70% and 90%. I would then use this number (for 70% it looks like its about 30) in the simpler calculation and prove that this number would give a 70% probability. I know this was really long and thank you for reading it! So basically my question is: would either one of these solutions give me enough Maths to get a good mark on Criterion E: use of mathematics? Or should I try using the Poisson approximation (Maths really isn't a strong subject for me though), or just find another approach altogether? My teacher isn't being particularly detailed in her emails and I have to give the draft in on the first day back at school, so I'd really like an opinion from someone else! Thank you so much in advance Reply Link to post Share on other sites More sharing options...
turtle turtle Posted May 11, 2015 Report Share Posted May 11, 2015 The paradox is very much about logic. Our teacher showed it us the basics of it in year 9 for fun, I don't think it's mathsy enough or a high enough standard/concept but ask your teacher Reply Link to post Share on other sites More sharing options...
erika_trxn Posted August 7, 2022 Report Share Posted August 7, 2022 On 4/14/2015 at 1:37 PM, beacohen97 said: (Sorry this is so long but really need urgent help! Draft due next week!) Hi everyone, So I've been stuck on my Maths IA for a while after having to change topics because my old one was too fiddly. I've discussed doing the Birthday Paradox with my teacher, and she said it was a good topic. However, I'm on holidays now and have sent her an email asking about a problem I was having and possible solutions. In her reply she said she was worried I wasn't doing enough maths. What I was previously planning on doing in the IA was: - Discussing the Birthday Paradox itself and the maths behind it (how many people do you need to have in a group so that there is an over 50% probability of 2 people sharing the same birthday - the answer is 23) - Using the maths of the paradox to calculate how many people you would need for that probability to be 70%, and then 90% - Investigate whether this works in real life by getting a random sample of 100 of my Facebook friends, and then randomly selecting the number needed for 70% and 90% probabilities and seeing whether it matches up (eg. if the answer for 70% was 30, I would do 10 random selections of 30 of the 100 Facebook friends and see whether 7 out of 10 trials had at least 2 people sharing a birthday) However, the problem I came across was to do with calculating the number needed for 70% and 90%. Most websites discuss the paradox by using the already known answer for 50% (23) and proving it using a relatively simple calculation. In order to find the number 23 itself, you need to use the Poisson approximation, which my teacher previously said would be too complicated. I thought that maybe I could get around this either: a) by selecting a number of people and finding the probability from there (although it would make it more complicated to investigate in terms of real life as it is unlikely it would be a round number like 70%) or b) Using a pre-made graph (which is reliable as the results appear the same on many different websites) of the probabilities from 0% to >99% to estimate the number of people needed for 70% and 90%. I would then use this number (for 70% it looks like its about 30) in the simpler calculation and prove that this number would give a 70% probability. I know this was really long and thank you for reading it! So basically my question is: would either one of these solutions give me enough Maths to get a good mark on Criterion E: use of mathematics? Or should I try using the Poisson approximation (Maths really isn't a strong subject for me though), or just find another approach altogether? My teacher isn't being particularly detailed in her emails and I have to give the draft in on the first day back at school, so I'd really like an opinion from someone else! Thank you so much in advance Hi, I know it's late but can you share your essay with me? I'm also doing my IA on birthday paradox and I have no idea what to write. Here's my gmail: [email protected] Reply Link to post Share on other sites More sharing options...
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