Byte Probability: Observing Three 1's and the First Bit

[brad sue]

Homework Statement

In a binary communication system all bit bytes are possible, and equally likely. Any bit is equallly likely to be a 1 or 0.
1- what is the probability of oberving a byte with exactly three 1's?
2-if a byte is observed with exactly three i's, what is the probability the first bit is a 1?

Homework Equations

combination formula nCp

The Attempt at a Solution

1- I did:
P(exactly three 1's)= C(3,8)/ 2^8

2-
Here I am confused:
I did P( three 1's and 1 is first)=C(2,7)/(2^8)
OR
P(three 1's and 1 is first)=C(3,7)/(2^8)
I cannot see which one is right.

Can someone tell me what I did right and wrong?
Thank you
B

 

[AlephZero]

2. Both your answers are wrong.

If there you know 3 bits are 1, then the question is the same as "you have a bag with 3 black balls and 5 white balls, what is the probablilty that the first ball you take out is black".

(If you can't see it, do the same problem with a 4-bit byte, and solve it by just writing out the 16 possibilities and counting them).