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evablogger [386]

3 years ago

10

Natalie visits a grocery store to buy tomatoes.The cost of tomatoes is $26.She remitted the bill and received $4 in change from

the cashier.How much she paid the cashier?

1 answer:

yKpoI14uk [10]3 years ago

5 0

$30
You need to add $4 to $26 since the tomatoes were 26 dollars and she received 4 back

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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.

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3 years ago

Which of the following statements are represented by

Anastaziya [24]

Answer:

"For every 6 windows I wash, I earn $2."

The ratio of windows washed to money earned is 3:1.

"For every 5 baseballs sold at the store, 7 footballs are sold."

The ratio of baseballs sold to footballs sold is 5:7

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3 years ago

Darius and Barb are playing a video game in which the higher score wins the game. Their scores are shown below.

Serhud [2]

Answer:

D. Darius is correct if only the median score is considered.

Step-by-step explanation:

5 0

2 years ago

On a trip to the movies a family spent $35 on tickets, and another $25 on popcorn. They also spent $10 on drinks. The oldest son

shusha [124]

The oldest son spent 6 dollars on candy.

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3 years ago

Read 2 more answers

Write the following set in roster form and in set-builder notation.

Vlad1618 [11]

Answer:

Roster Form of M = {-2, -1 , 0, 1}

Set Builder Form of M = {x : x is an integer and -3 < x ≤ 1 }

Step-by-step explanation:

Roster Form: A set is said to be in roster form if each element of the set is written distinctly in the set with commas in between them.

Set Builder Form: A set is said to be in set builder form if all the set elements are represented by describing their properties.

Now, here M is the set of integers that are greater than -3 and less than or equal to 1.

So, by definition of the set forms,

Roster Form of M = {-2, -1 , 0, 1}

Set Builder Form of M = {x : x is an integer and -3 < x ≤ 1 }

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4 years ago