Calculating Probability of Getting 3 Heads in a Row in 64 Tosses

  • Thread starter Thread starter Yura
  • Start date Start date
  • Tags Tags
    Probability
AI Thread Summary
To calculate the probability of getting three heads in a row in 64 tosses, one must first understand the basic probabilities of single and multiple tosses. The probability of getting heads in one toss is 0.5, and this can be extended to calculate the probabilities for two and three tosses. For more complex scenarios, such as finding the probability of two or three heads in a row within a larger number of tosses, it is essential to determine the sample space by considering all possible outcomes. The discussion emphasizes the importance of systematically analyzing smaller cases before applying combinatorial methods like nCr and nPr. Understanding these foundational concepts is crucial for accurately calculating the desired probability.
Yura
Messages
37
Reaction score
0
my brother needs to know this but I'm in exam block right now and can only think of the physics I am studying this term. i can't remember how to figure this out anymore i just know i'll have to use nCr and nPr.
heres the question:
how do i find the probability of getting tossing 3 heads in a row out of 64 tosses?

thanks
 
Last edited:
Physics news on Phys.org
Suppose you had one toss only. What is the prob. of a head?

Suppose two tosses. What is the prob. of 2 heads?

Suppose 3 tosses. What is the prob. of 3 heads?

Now, the hard one: in 4 tosses, what is the prob. of one head only? The prob. of 2 heads (regardless of their order)?

The really difficult ones: with 4 tosses, what is the prob. of 2 heads in a row? 3 heads in a row?
 
Last edited:
1st find the desired sample space ie: how many ways are there to have 3 heads in a row out of 64 tosses? don't rush to nCr and nPr just now, think about the possibilities.
then find the total number of possibilities and use the definition a probability.
 
To find the sample space you might start from just one toss, then 2 tosses, then 3, 4, ... etc. and make a list of all possible outcomes for each case.
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
Back
Top