Probability Formula?

humannn

Dormant account
Joined
Mar 15, 2006
Location
Lisbon
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

Dormant account
Joined
Jan 21, 2004
Location
UK
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

Dormant account
Joined
Mar 15, 2006
Location
Lisbon
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

Ueber Meister
PABnonaccred
CAG
Joined
Dec 1, 2005
Location
Denmark
humannn said:
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
 
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