Question

SHOW WORK!!!!! Full credit will not be given for answers only. NOTE: for any question asking you to determine a probability---- you MUST write out a probability statement using proper notation!!!! Probabilities should be DECIMAL form and rounded to 4 decimal places. 1. There are several scenarios described below. For each of them, do the following (note: R.V. means random variable) (1) Define the R.V.--- that means something like, "Let X be the number of people who....." (2) Define the distribution and parameter(s) of the R.V. (3) Give the support of the R.V. (4) Write the probability statement related to the information being sought. Do not calculate the probability. a) Joe is debugging a coding project. From prior experience he expects to find a bug in every 25 lines of code and each bug occurs independently of other bugs. What is the probability that it takes more than 30 lines of code until Joe finds his first bug? b) Joe has examined 500 lines of code and has identified several bugs. What is the probability that the next line that Joe examines contains another bug? c) Joe will keep working until he has identified 15 bugs. What is the probability that Joe examines exactly 400 lines of code before Joe takes a break? d) The current project Joe is debugging contains 1200 lines of code. Determine the probability that he finds more than 52 bugs in the project. e) A previous project is currently running live and will continue to run until it runs into a serious error. A serious error occurs on average once every 90 days. Determine the probability of observing at least 3 serious errors in an eight-month period (assume 30 days in a month and that the project restarts immediately). f) After a long day of debugging Joe decides to have a few beers at his local brewery. The brewery has 15 different beers on tap, 13 of which have alcohol content less than 7%. If Joe decides to randomly have four different beers find the probability that 3 of the beers have alcohol content less than 7%.

Answer 1

I will answer first 4 since there are more than 4 sub parts

(a)

let X be no. of lines before any bug is found

P(bug in any line) = 1/25

P(bug not in line) = 1 - 1/25 = 24/25

P(x) = (P(bug not in line))x

P(30) = (24/25)^30 = 0.2938

(b)

P(next line conatins bug) =  P(bug in any line) = 1/25

(c) for 15 bugs to be in exactly 400 lines

400th line ahs bug and previous 399 lines have 14 bugs in any arrangement

P(400th line has bug) = P(bug in any line) = 1/25

P(14 bugs in 399 lines) = 399C14(P(bug in line)14)(P(bug not in line)385) = 0.0946

P(15 bugs in exactly 400 lines) = P(14 bugs in 399 lines) * P(400th line has bug) = 0.0946 * 1/25 = 0.0037

(d) P(x bugs in y lines) = yCx(P(bug in line)x)(P(bug not in line)y-x)

P(x>52 bugs in 1200 lines) = P(53 bugs in 1200 lines) +  P(54 bugs in 1200 lines) +  P(55 bugs in 1200 lines) + .....+ P(1200 bugs in 1200 lines) = 0.2496

P(x>52 bugs in 1200 lines) = 0.2496

P.S. (please upvote if you find the answer satisfactory)