First Post :P Anyways, here's a problem I've been pondering.

This was on a math contest that I wrote a couple days ago, and the answer's bugged me ever since.

If you flipped 10 coins, what is the probability that two or more consecutive flips will be heads?

I have 2 different theories, let's see what you guys come up with.

EDIT: Please JUSTIFY your answer, and don't just post it.

 

omg I hate the probability things... I can never get them right, but I have a probability simulator on my calculator and I use it in math class all the time

 

TI 83/84?

Our school made us buy those 120 dollar pieces of crap. Staples sells $20 graphing calculators that won't get stolen as much. I've had 3 of the 120 dollar a piece ones stolen =/

I love probability. I feed of it like blood. *Laughs evilly*. Honestly though, I read this book, 300 pages or something, about the statistics that run our world. Found it really interesting. Bahaha I'm such a dweeb.

 

I have a TI-83 PLUS Platinum Edition...lmao the got so fancy with their new calculators... platinum *bling bling*

 

1:4 is the answer.

 

That's the probability if you flipped just 2 coins, of them both being heads. But we're flipping 10, remember?

 

answer:
1:16

 

ooo, i guess i should have read thr problem. its a very good chance then, probably around 4:5. dont feel like finding my calc right now

 

Here's the way I see it, correct me if you think I'm wrong.

The only way to NOT get 2 consecutive flips of EITHER heads or tails is for every other one to be heads or tales. That will have a chance of 1 in 1024, since 1/2^10 is 1/1024. That means that the chance of having 2 in a row of whatever you're calculating is 1023/1024. Then, you want heads, so halve this figure. 511.5/512.

 

Just read your edit; justify it.
Since your flipping 10 coins once, each coin has a possibility of 1/2 of getting heads. Since the question is asking what is the probability that two or more consecutive flips that will be heads, each event is independant, therefore not affecting each other.

Probability of getting 2 heads from two coins: 1/4
The probability of getting two/more consecutive head flips = 1/16.
The probability 511.5/512 is considered wayy to high. I'm no expert though.

 

ooo yay a homework board
uhhh i suck at probabilty but im good in math
of course im only in grade 8
sorry i couldnt help

 

Wow. I have no clue, sorry.
But my dad majored in math.
-scratches head-
Maybe I got my moms smarts

 

1/2 because theres a 50/50 chance that it could be heads or tails.

 

I don't really think it's too high =/ I think 1 in 16 is far too low. If the probabilty of getting 2 heads in 2 flips is 1:4, wouldn't the probabilty of getting 2 consecutive heads in 10 flips be higher, since you're doing it more times?

 

Ah, so that's how you're approaching it.
No, the probability of getting 2 consecutive heads won't be higher. It doesn't matter if there's 20 coins; as long as you're flipping each coin once, if it's the same question, it's still 1/16.
The way you're probably thinking, is what's the probability of every coin flipped will have heads 2x consecutively.
Do you by chance have access to the answer? I'm pretty positive it isn't anywhere near triple digits, and something like 1:16. These questions get even more annoying if it was like, 'what's the etc..... when flipping 10 coins 5 times?'

 

No, I don't have the answer, that's why I'm asking.

It has to be more than 1/16. I just did the test 5 times, and got it within 5 flips on all 5 of them. Sure, it's not a big sample, but it's more than 1/16 for sure.

 

the odds are going to be better than 1:4 because you have more chances to get 2 in a row, not just 2. instead of halving both sides, just half the result side.

511.5/1024

 

O this is fun....Wats The square root of 1742681324

 

~4175.507

but was that relevant?

 

U got me there bititido !!!