Mathematics, 24.03.2020 01:27 cajunldy2001

Suppose that bugs are present in 1% of all computer programs. A computer de-bugging program detects an actual bug with probability 0.99, but falsely detects a nonexistent bug with probability .02. Give numerical answers to each of the following questions:

(i) If the de-bugging program claims to have found a bug in program A, what is the probability that the bug is actually present?

(ii) Suppose that Program A is tested twice, the two tests conducted independently. If the de-bugging program claims that bugs are present on both the first and second tests, what is the probability that a bug is actually present?

(iii) Suppose that Program A is tested three times, the three tests conducted independently. If the de-bugging program claims that bugs are present on all three tests, what is the probability that a bug is actually present?

Answers: 1

Show answers

Answers

(i) The probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

Step-by-step explanation:

Denote the events as follows:

B = bugs are present in a computer program.

D = a de-bugging program detects the bug.

The information provided is:

$P(B) =0.01\\P(D|B)=0.99\\P(D|B^{c})=0.02$

(i)

The probability that there is a bug in the program given that the de-bugging program has detected the bug is, P (B | D).

The Bayes' theorem states that the conditional probability of an event E given that another event X has already occurred is:

$P(E|X)=\frac{P(X|E)P(E)}{P(X|E)P(E)+P(X|E^{c})P(E^{c})}$

Use the Bayes' theorem to compute the value of P (B | D) as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D|B)P(B)+P(D|B^{c})P(B^{c})}=\frac{(0.99\times 0.01)}{(0.99\times 0.01)+(0.02\times (1-0.01))}=0.3333$

Thus, the probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii)

The probability that a bug is actually present given that the de-bugging program claims that bug is present is:

P (B|D) = 0.3333

Now it is provided that two tests are performed on the program A.

Both the test are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is:

P (Bugs are actually present | Detects on both test) = P (B|D) × P (B|D)

$=0.3333\times 0.3333\\=0.11108889\\\approx 0.1111$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii)

Now it is provided that three tests are performed on the program A.

All the three tests are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is:

P (Bugs are actually present | Detects on all 3 test)

= P (B|D) × P (B|D) × P (B|D)

$=0.3333\times 0.3333\times 0.3333\\=0.037025927037\\\approx 0.037$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

Answer from: Quest

Arhombus is a quadrilateral.

Answer from: Quest

answer: sorry i can't you.

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Clara schumann is buying bagels for her coworkers, she buys a dozen bagels priced at $5.49 a dozen. the bakery's cost for making the bagels is $2.25 per dozen. what is the markup rate based on selling price on a dozen bagels?

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

10 points? me . its important ‼️‼️

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

60 musicians applied for a job at a music school. 14 of the musicians play both guitar and drums. what is the probability that the applicant who gets the job plays drums or guitar?

Answers: 1

Answer

You know the right answer?

Suppose that bugs are present in 1% of all computer programs. A computer de-bugging program detects...

Questions