Proving Summation nCk p^k q^n-k =1

[sajee3a]

1)given that: (1+x)^n=summation nCk X^K

PROVE: SUMMATION nCk p^k q^n-k =1, where p+q=1
2) prove the general law of addition: P(E1 U E2 U...U En)=sum P(Ei)-sum P(EiEj)+sum P(EiEjEk)-...(-1)^n-1 P(E1E2...En)

 

[mathman]

For 1:
1=(p+q)ⁿ=qⁿ(1+(p/q))ⁿ=qⁿΣnCk(p/q)^k=ΣnCkp^kq^n-k