Probability Formula?

[humannn]

Hi Everyone:

I'd like to know the formula for figuring out the probability of getting an X number of "tails" in a row (e.g. you have a 4 percent chance of flipping tails five times in a row). But what does the math actually look like?

I used a coin as an example, but it could also apply to Craps, Roulette, Blackjack, etc.

Thank you.

 

[GrandMaster]

If the probability of an event is p, then the probability of it happening n times in a row is p^n (p to the power of n). In the case of a coin toss, p=1/2, so the probability of 5 tails in a row is 1/2^5=1/32=0.03125=3.125%.

 

[humannn]

Thank you for the answer, GrandMaster.

So the 3.125% figure would be the odds of flipping tails 5 times in a row out of only 5 total flips, correct? Slim odds, indeed. Do you know how to figure out how many times 5 in a row would occur in an x number of flips? Say 100?

 

[Zoozie]

Do you know how to figure out how many times 5 in a row would occur in an x number of flips? Say 100?

T=tail

You need to specify this a little more precise. Do you mean flip a coin 100 times and then count number of times you have 'blocks' with TTTTT
If you hit 10 T's in a row, do this only count as 1 or actually as 5? What if you hit 7 T's in a row etc.

Maybe you mean the following: what is the probability that 5 T's will occur (once or more) in a row when you flip a coin 100 times.
I ran a simulation for this problem and it gave:

total number of succes:9721241
total game starts:12000000 (I ran 12M simulations each of flipping a coin 100 times)
Probability:0.8101 (81.01%)

I can change the following parameters if this simulation is usefull to anyone.
I generalized it to throwing a n-sided dice and counting the max number instead of flipping a coin. The problem seems hard to solve excact with math, so it was
much faster to just simulate it.

numberInARowNeeded=5;
numberOfTries=100;
sidesOnDice=2;


Zoozie