Probability Question (Random Variables and CDF)

[swuster]

Homework Statement

A transmission channel is noisy and a binary bit (assume it is a 0 or a 1) has probability of .11 of being incorrectly transmitted. Suppose the bit is sent n (odd) times and a majority decoder announces which bit is received the majority of the time. Assume retransmissions constitute Bernoulli trials.
(a) Let X be the number of errors in n transmissions. Give a formula for the distribution of X.
(b) What is the probability the message is correctly received, for n=25?

Homework Equations

n/a

The Attempt at a Solution

X is discrete, so for part (a) I came up with $$p_{x}(x)=.11^{x}.89^{n-x}$$ which I'm not convinced is totally right.

For part b I want to calculate $$P(X\leq12)$$ since this is the probability that the message is correctly received (number of errors is less than half). But if I attempt to calculate the cumulative distribution function using my distribution, I get $$\sum^{12}_{x=1}.11^{x}.89^{n-x} = .06195$$ which is clearly way too low. Any help?

 

[annoymage]

hmm, I really confused with the words (my english fault). anyway, what i know about bernoulli's trial is that there's only chance of sucess and failure..

So, the equation of bernoulli's trial f(x)=(p)^x(1-p)^1-x , x=0,1

so, in this case,
f(x)=(ⁿC_x)(0.11)^x(0.89)^n-x , x=1,2,...,n

because of n times,