Verify Probability & Expected Score for 2 Quick Problems

[johnstamos]

Hey guys, having a bit of trouble and can't find anyone to double check my work:

Mean failure rate of a communication is 1 error per 10 000 000 characters transmitted.
If an error occurs, there is a probability p that it will be discovered and corrected. What is the probability no errors occur after N characters are transmitted.

Rate= N/10 000 000*(1-p)?

So the chance that an error occurs multiplied by the probability that it is not corrected.

I'm unsure of how exactly my rate would change.

P(X=0) = Poissoin(X=0,Rate as stated above). This problem seems simple enough, but again, the rate is messing me up here.Second question: X~GEO(1/5). The game ends when a success occurs. When the success occurs, the user wins 100. Every other time he loses 20. What is the expected total score.

I assume it's Y=120-20X. So E(Y) = 120-100=20. I've seriously had a tonne of people give me varying answers and that's probably why I'm so confused.

Could anyone verify these things quickly? I've done most of the legwork so hopefully this doesn't come off as a pathetic attempt for you to do my homework.

Regards

 

[Valkarie]

,For the first question, the rate would be N*(1-p)/10 000 000. So the probability that no errors occur after N characters are transmitted would be Poisson(X=0, Rate=N*(1-p)/10 000 000).For the second question, your calculations are correct. Your expected total score is 20.