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/sci/ - Science & Math

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1733512 No.1733512 [Reply] [Original]

Why is it that the chances of getting 100 tails in a row is less than getting 50 heads and 50 tails? If it's a 50-50 chance of getting a head, then the next flip will also be 50-50, and subsequently the next one would be too. Therefore, the chances of getting 3 heads in a roll would be 50-50, just as the chances of getting 1 head and 2 tails would be the same, right?

>> No.1733531

That question is bad and you should feel bad.

>> No.1733533

Because probability says so.

(1/2)^100 < (1/2)^50

>> No.1733538

lrn2binomial

>> No.1733541

>>1733512
Getting them in an exact order is the same as getting 100 tails, though.

Understanding probability requires some good maths, or the right perspective.

>> No.1733548

What you need to do is a draw a tree with all possible outcomes - branches after each flip

>>heads>>heads
heads >>tails
>>tails>>heads
>>tails

add up all the lines write down the total
add up all the lines with 50 heads + 50 tails
add up all the lines with 100 tails

I find a good way to set it out is to use excel.

>> No.1733554

>>1733548

          >>heads>>heads
heads              >>tails
          >>tails>>heads
                      >>tails

>> No.1733557

>>1733548
After that, though, can't you just pick and choose which path you want and the probability will be the same?

>> No.1733569

Getting 100 tails in a row has the same probability of a head, then a tail, then a head, then a tail etc. for 100 times, but not 50 tails/heads without a specific order

>> No.1733576

Think of it this way:

Each flip has a chance of being heads and a chance of being tails. There are a great many combinations of chances that result in 50 heads and 50 tails total, but there is only one combination that results in 100 tails.

>> No.1733578

>>1733576
You're my hero.
Thanks man

>> No.1733643

any time <3

>> No.1733807

Think it like this: u can get 50 tails in row and then 50 heads, but u can also get 49 tails in row, then 50 heads, then 1 tail. U can also get 20 tails, 1 heads, 29 tails, 42 heads, 1 tail and 7 heads. Its still the same. The amount of different ways u can put 50 tails and 50 heads is roughly 10^29.

>> No.1733830

arent the odds of getting that the same as the odds are of getting any other combination of 100 coin flips?

>> No.1733833

>>1733830
The probability of getting any unique combination of heads and tails is the same.

If one pattern can be realized in many ways (eg 40 heads total or something like that), it's obviously more likely to happen.