Solve each equation for the given variable.<br> 1.<br> x

Suppose that bugs are present in 1% of all computer programs. A computer de-bugging program detects an actual bug with probabili

lawyer [7]

Answer:

(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:

<em>B</em> = bugs are present in a computer program.

<em>D</em> = 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 <em>E </em>given that another event <em>X</em> 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.

4 0

3 years ago

Mya had 12 assignments to complete by Friday of this week. So far, she completed 75% percent of her assignments this week. How m

lesya692 [45]

Answer:

3 assignments incomplete.

Step-by-step explanation:

context: 75% can be rewritten as 0.75

12 × 0.75 = 9 assignments completed.

The above equation shows the amount of assignments that have been already completed. In order to find out how many assignments she has yet to have completed, we need to subtract these amounts.

12 - 9 = 3 assignments incomplete.

5 0

3 years ago

What are the solutions to the quadratic equation 4x2 = 64?

Karolina [17]

<h2>Greetings!</h2>

Answer:

x = −4 and x = 4

Step-by-step explanation:

4x² = 64

Lets get x² on its own. To do this we divide each sides by 4:

x² = 16

Now to get just x, we need to square root this answer:

√x² = √16

x = √16

x = 4

But this can be ±4 as it -4 and 4 squared both give 16.

So your answer is x = −4 and x = 4

<h2>Hope this helps!</h2>

7 0

3 years ago

Read 2 more answers

Simplify -14x > -3 please needed very fast please

Paladinen [302]

Answer:x < 3/14

Step-by-step explanation:

-14x > -3

x < 3/14

8 0

3 years ago

Read 2 more answers

Line m is parallel to line n. The measure of angle 2 is 64°. What is the measure of angle 5?

zloy xaker [14]

Angles 2 and 6 are corresponding angles.
When parallel lines are cut by a transversal, corresponding angles are congruent, so angles 2 and 6 are congruent.
m<2 = m<6 = 64 deg.

Angles 5 and 6 are a linear pair, so they are supplementary, and their measures add to 180 deg.

m<5 + m<6 = 180

m<5 + 64 = 180

m<5 = 180 - 64

m<5 = 116

Answer: m<5 = 116 deg.

4 0

4 years ago

Solve each equation for the given variable. 1. x - 17 = 28