RIGHT AWAY, I must warn you to NOT TRUST any answers given. THEY ARE ALL WRONG!
First of all, congratulations on asking a really tricky question. Well, determining the PROBABILITY is actually easy! The tricky thing to do is to determine THE PATTERNS!
FIRST, lets set up the equation, and SECOND, lets talk about patterns ok!
FIRST, to set up your equation, we need to know our sample space. In other words, we need to know "HOW many total possible outcomes can occur if we flip a coin 250 times."
Well, that is very easy right? Think about it, we have one coin that can land two ways, either heads or tails, right? Therefore, since we are flipping the coin 250 times, the total possible outcomes are 2^250 = 1.427xE45.
This is an EXTREMELY HUGE NUMBER, and this will go into our denominator.
Therefore, we can now set up our equation.....
X / 1.427xE45 = Our Answer.
NOW, YOU are probably wondering what X will be right? Ok, this is where we now talk about PATTERNS!
This is where your problem gets really tricky, and requires advanced mathematics skills.
Well, to find X, we have to determine EXACTLY how many different ways we can get 8 heads in a row, from flipping a coin 250 times. This becomes very tricky, and I will show you how tricky this can get.
Well, we are basically trying to figure out ALL the possible PATTERNS of getting 8 heads in a row (OR MORE) from flipping a coin 250 times. Here are some possible patterns:
8 heads, then 242 tails
8 heads, then 241 tails, then 1 head
8 heads, then 240 tails, 2 heads
OR, these are also possible patterns
8 heads, then 2 tails, then 8 heads, then 2 tails, then 230 heads
8 heads, then 2 tails, then 8 heads, then 3 tails, then 229 heads
OR, what about these patterns....
15 tails, then 30 heads, then 3 tails, then 12 heads, then 190 tails
OR what if they all turn out to be ALL 250 HEADS?
As you see, there are an ENORMOUS amount of different ways you can get 8 heads in a row from flipping a coin 250 times. Therefore, the only way to figure out the answer to your problem would require someone to be EXCELLENT AT figuring out EVERY POSSIBLE PATTERN of getting AT LEAST 8 heads in a row out of 250 coin flips.
Therefore, everyone else is WRONG. The equation I have above is the right equation, however, it requires ADVANCED MATHEMATICS to determine exactly all the possible patterns of 8 or more in a row. My math skills are only up to Calculus One, however, to solve this problem will often require someone who has completed Calculus 1,2,and 3, and have also taken a Probability based Calculus course!
Well, as I further my studies, I will eventually be able to solve your problem with ease. Good luck!
I love math!
· 1 decade ago