Answer:
The probability that it takes more than 30 lines of code until Joe finds his first bug is 0.2821.
Step-by-step explanation:
Let X = number of bugs in every 25 lines of code.
The probability of the random variable X is, [tex]P(X)=p=\frac{1}{25}[/tex].
The random variable X follows a Geometric distribution.
A Geometric distribution is the probability distribution of the number of Bernoulli trials needed before the first success.
The probability mass function of Geometric distribution is:
[tex]P(X=x)=(1-p)^{x-1}p; x=0,1,2,3...[/tex]
Compute the probability that it takes more than 30 lines of code until Joe finds his first bug as follows:
P (X > 30) = 1 - P (X ≤ 30)
[tex]=1-\sum\limits^{30}_{x=0}[(1-\frac{1}{25})^{x-1}\frac{1}{25}]\\=1-0.7179\\=0.2821[/tex]
Thus, the probability that it takes more than 30 lines of code until Joe finds his first bug is 0.2821.
