$MathMaster logo$

MathMaster

Home
general
if faults in cars are reported correctly 85 of the time but it is known that 35 are reported as faults when it was really

Question

If faults in cars are reported correctly 85% of the time, but it is known that 35% are reported as faults when it was really due to poor handling, even 30% if they are due to faults, calculate the probability that yes be it due to failure when it was reported that way

297

likes

1483 views

Answer to a math question If faults in cars are reported correctly 85% of the time, but it is known that 35% are reported as faults when it was really due to poor handling, even 30% if they are due to faults, calculate the probability that yes be it due to failure when it was reported that way

$Expert avatar$

4.5

104 Answers

1. Calculate the probability of no-fault reports:

P(A^c) = 1 - P(A) = 1 - 0.30 = 0.70

2. Calculate the total probability of a report:

P(B) = P(B \mid A) P(A) + P(B \mid A^c) P(A^c) = (0.85 \cdot 0.30) + (0.35 \cdot 0.70) = 0.50

3. Use Bayes' theorem to calculate the probability of an actual fault given a report:

P(A \mid B) = \frac{P(B \mid A) P(A)}{P(B)} = \frac{0.85 \cdot 0.30}{0.50} = 0.51

Frequently asked questions (FAQs)

Question: Find the square root of (-12) and express it in the form a + bi, where a and b are real numbers.

+

Question: Find the vertex of the quadratic function y = -2x^2 + 4x - 1.

+

Math Question: What is the derivative of f(x) = 3x^2 - 4x + 2?

+

New questions in Mathematics

5 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight

³√12 x ⁶√96

Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]

4x-3y=24 and 5x-2y=9 solve by elimination

(24, -7) is on the terminal arm of an angle in standard position. Determine the exact values of the primary trigonometric functions.

Primes are numbers divisible only by 1 and themselves; There are infinitely many prime numbers and the first ones are 2, 3, 5, 7, 11, 13, 17, 19, 23, .... Consider a 12-sided die, with the faces numbered from 1 to 12. Out of 4 rolls, the probability that only the first three numbers are primes is:

A box of numbered pens has 12 red, 12 blue, 12 green and 12 yellow pens. The pens for each colour are numbered from 1 to 12. There is a unique number on each pen, so no pen is exactly the same as any other pen in the box. When reaching into the box to randomly draw five pens without replacement, what is the proportion of getting exactly four pens of the same colour (Note: the numbers matter but the order does not)?

Shows two blocks, masses 4.3 kg and 5.4 kg, being pushed across a frictionless surface by a 22.5-N horizontal force applied to the 4.3-kg block. A. What is the acceleration of the blocks? B. What is the force of the 4.3-kg block on the 5.4 -kg block? C. What is the force of the 5.4 -kg block on the 4.3 -kg block?

ind the z-score for which 72% of the distribution's area lies between -z and z. -1.7417, 1.7417 -1.1538, 1.1538 -1.0803, 1.0803 -2.826, 2.826

A contractor gives a bank note for $10250 at a rate of 1% for one month. How much interest is charged for 4 months?

9/14 x 7/27 carry out indicated operation

Translate to an equation and solve. Let x be the unknown number: What number is 52% of 81.

Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)

If sin A=0.3 and cos A=0.6, determine the value of tan A.

Read the “Local Communities as Stakeholders: Does Amazon Really Need Tax Breaks?” example on p. 83 in Ch. 3 of Management: A Practical Introduction. In your response, discuss whether you feel that tax breaks for big companies benefit local communities. Describe ways to attract business to a region without having a negative impact on the larger community.

Square root of 169 with steps

An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?

In a cheese factory, one pie costs 3800 denars. The fixed ones costs are 1,200,000 denars, and variable costs are 2,500 denars per pie. To encounter: a) income functions. profit and costs; b) the break-even point and profit and loss intervals.