Average Times Coin Combination Appears in 10 Letters

[ParisSpart]

Flipping a fair coin 10 times. This creates a word of length 10 of the letters C and L. On average how many times it appears in this sub-word CCLLCC?
C=crown and L= the other side of coin

i think that if i count CCLLCC in 10 letters of C and L we will have 5 times but how i will find the average?

 

[HallsofIvy]

If 6 of the letters are "CCLLCC" then the other four letters can be either "C" or "L". There are 2^4= 16 ways to do that. But you also need to allow for where in the set of 10 letters those letters occur.

I assume by "sub-word", you require that the letters "CCLLCC" occur together. Do you see that there are 5 places the initial C can be?

 

[Ash L]

Hello, I'm not quite sure if I'm right as I'm still a novice in the world of math. It's been a while since I have taken my prob/stats class.

__ __ __ __ __ __ __ __ __ __

There are 2 ways either C or L for each of the spaces above. So, the total number of ways for spelling out a 10 letter word is 2*2*2*2... = 2^{10} = 1024

There are 5 ways for CCLLCC to occur inside some of the 10 letter words. One of them looks like this:

C C L L C C __ __ __ __

The spaces containing CCLLCC are all "locked in". So, there are 4 spaces left for choices.

2*2*2*2 = 2^{4} = 16
There are 5 ways in which CCLLCC can occur because you can just shift CCLLCC one space to the right each time to get a new word that contains CCLLCC.

Possible ways of getting a word with CCLLCC in it: 5*16 = 80

I'm not sure what you meant by "average", so I guess you want the probability as well. \frac{80}{1024} = 0.0781

Once again I'm not a 100% sure, but I hope it helps you a bit. :P