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

[Yura]

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

 

[EnumaElish]

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?

 

[hello3719]

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.

 

[EnumaElish]

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.