Discussion Forum

More and more Evidence (Weekly Brain Potion Discussion)

 
 
Lensmire John的相片
More and more Evidence (Weekly Brain Potion Discussion)
Lensmire John發表於2017年 11月 10日(Fri) 15:56
 

At lunch your friend calls you over to see the silver dollar he got while on vacation. He showed you the front (heads) and the back (tails) and said it was really fun to flip.

You watched your friend flip the coin and get tails. He flipped it again and again got tails. He said, "Wow, let's see how many times I can get tails in a row!" Third flip, tails; fourth flip, tails! In fact your friend flipped the coin ten times in a row and got all tails!

Before he flipped the coin the eleventh time, you wondered, "What is the chance that the next flip is tails?"

Please share any thoughts or questions you have below. We'll monitor the responses and give our thoughts as well!

 
Liu Anna的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
Liu Anna發表於2017年 11月 11日(Sat) 20:51
 

1/2, I think, because the previous attempts don't affect the current attempt. He can get either heads or tails, and the outcomes are equally likely. And while it is still unlikely that he gets 10 tails in a row, he has a 1/2 probability for each flip.

Fang Jeffrey的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
Fang Jeffrey發表於2017年 11月 12日(Sun) 10:14
 
We have no idea if the coin is fair. This could mean the probability could be anything from 0 to 1
def abc的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
def abc發表於2017年 11月 23日(Thu) 08:09
 

um... It cant be 0. Otherwise it is impossible to get the previous 10 attempts of all heads.

Chen Jeffrey的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
Chen Jeffrey發表於2017年 11月 12日(Sun) 11:10
 

If there really was a half chance of flipping tails 10 times in a row, then the chances of flipping a tail is 1/x, where x^10 equals to 2. The problem also did mention that the coin was really fun to flip, so it is probably not a fair coin

weng Allen的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
weng Allen發表於2017年 11月 12日(Sun) 15:03
 

As stated before, we have no idea is the coin is fair. Though it seems like tails must be next, as far as we know the coin is rigged to display tails 10 times and heads on the 11th.So more information is needed to solve this problem.

wu Christopher的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
wu Christopher發表於2017年 11月 12日(Sun) 17:38
 
Wouldn't this just be the tenth root of 1/2? as there is a chance that the probability of tails is very low, but a much higher chance that it is very high, and it should end up x^10=1/2 on average. It could by 100%, or 1 %, but 100 is far more likely, and it balances out in the end.

so around 93.3033


wu Christopher的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
wu Christopher發表於2017年 11月 22日(Wed) 13:32
 

Even if the coin is fair, the way your friend flips it could be rigging it. If you start with tails up, it is more likely to be tails. With some skill, he could raise this probability. 

W Terry的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
W Terry發表於2017年 11月 12日(Sun) 19:25
 

Assuming that the coin is fair and that they're using the same coin for the 11th flip, then the probability is 1/2 because they are independent events. Now if the coin is somehow rigged, then we do not know the outcome.

Zhao Ray的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
Zhao Ray發表於2017年 11月 19日(Sun) 06:31
 

half

def abc的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
def abc發表於2017年 11月 23日(Thu) 08:07
 

I think that the chance of flipping a tail is a half of a chance. Even though flipping 10 times, and all of them are heads, the chances of flipping heads and tails are still the same.

wu Christopher的相片
Re: More and more Evidence (Weekly Brain Potion Discussion)
wu Christopher發表於2017年 11月 23日(Thu) 08:52
 

The coin may not be fair