The probability that a one-car accident is due to faulty brakes is 0.04, the probability that a one-car accident is correctly attributed to faulty brakes is 0.82, and the probability that a one-car accident is incorrectly attributed to faulty brakes is 0.03. What is the probability that (a) a one-car accident will be attributed to faulty brakes; (b) a one-car accident attributed to faulty brakes was actually due to faulty brakes?

Danika Mckay 2022-10-24 Answered
The probability that a one-car accident is due to faulty brakes is 0.04, the probability that a one-car accident is correctly attributed to faulty brakes is 0.82, and the probability that a one-car accident is incorrectly attributed to faulty brakes is 0.03. What is the probability that (a) a one-car accident will be attributed to faulty brakes; (b) a one-car accident attributed to faulty brakes was actually due to faulty brakes?
Is my work below correct?
My Approach:
Event A- Car accident is due to faulty break
Event B- It gets correctly attributed to faulty break
Event D- It gets incorrectly attributed to faulty break
Event C- It gets attributed to faulty breaks ; then
P ( A ) = 0.04
P ( B ) = 0.82
P ( D ) = 0.03
P ( A ) = 0.96
(a) I use total probability rule i.e.
P ( C ) = P ( A ) P ( B | A ) + P ( A ) P ( D | A )
P ( c ) = ( 0.04 ) ( 0.82 ) + ( 0.96 ) ( 0.03 )
P ( C ) = 0.0328 + 0.0288
P ( C ) = 0.0616
(b) For this I used Bayes theorem;
P ( A | C ) = P ( A n C ) / P ( C ) = P ( A ) P ( C | A ) / P ( C ) = ( 0.04 ) ( 0.82 ) / 0.0616 = 0.0328 / 0.0616
P ( A | C ) = 0.532467532
You can still ask an expert for help

Want to know more about Probability?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

blogpolisft
Answered 2022-10-25 Author has 10 answers
Step 1
There are two circumstances, "attribution to faulty brakes" and "has faulty brakes". Let's call these events A and F. Then you should write
P ( F ) = 0.04 P ( A | F ) = 0.82 P ( A | F ) = 0.03
Step 2
The things you're asked to calculate are:
(a) A one car accident will be attributed to faulty brakes
P ( A ) = P ( A | F ) P ( F ) + P ( A | F ) P ( F ) = 0.82 × 0.04 + 0.03 × 0.96 = 0.0616
and
(b) a one-car accident attributed to faulty brakes was actually due to faulty brakes
P ( F | A ) = P ( A , F ) P ( A ) = P ( A | F ) × P ( F ) P ( A ) = 0.04 × 0.82 0.0616 = 0.532...
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-08-20
Let X be a normal random variable with mean 12 and variance 4. Find the value of c such that P{X>c}=.10.
asked 2021-08-19
Based on the Normal model N(100, 16) describing IQ scores, what percent of peoples
asked 2021-08-19
Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times.
What are the possible values of X?
asked 2021-10-21
The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.
Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood.
asked 2021-01-02
Suppose you roll a number cube. Find the probability. P(3 or 4)
asked 2021-08-15

The game of Clue involves 6 suspects, 6 weapons, and 9 rooms. One of each is randomly chosen and the object of the game is to guess the chosen three. (1) How many solutions are possible? In one version of the game, the selection is made and then each of the players is randomly given three of the remaining cards. Let S, W, and R be, respectively, the numbers of suspects, weapons, and rooms in the set of three cards given to a specified player. Also, let X denote the number of solutions that are possible after that player observes his or her three cards. (2) Express X in terms of S, W, and R. (3) Find E[X]

asked 2022-02-12
A box contains 11 marbles, 7 red, and 4 green. Five of these marbles are removed at random. If the probability of drawing a green marble is now 0.5, how many red marbles were removed?

New questions

i'm seeking out thoughts for a 15-hour mathematical enrichment course in a chinese language high faculty. What (pretty) simple concern would you advocate as a subject for any such course?
historical past/issues:
My students are generally pretty good at math, but many of them have no longer been uncovered to rigorous or summary mathematical reasoning. an amazing topic would be one that could not be impossibly hard for students who have by no means written or study proofs in English.
i have taught this magnificence three times earlier than. (a part of the purpose that i'm posting that is that i have used up all my thoughts!) the primary semester I taught an introductory range theory elegance (which meandered its way toward a proof of quadratic reciprocity, though I think this become in the end too advanced/abstract for some of the students). the second one semester I taught fundamental graph idea and packages (with a focal point on planarity and coloring). The 1/3 semester I taught a class at the Rubik's dice.
the students' math backgrounds are pretty numerous: a number of them take part in contest math competitions, and so are familiar with IMO-fashion techniques, however many aren't. a number of them may additionally realize some calculus, however I cannot assume it. all of them are superb at what in the united states is on occasion termed "pre-calculus": trigonometry, conic sections, systems of linear equations (though, shockingly, no matrices), and the like. They realize what a binomial coefficient is.
So, any ideas? preferably, i'd like to find some thing a bit "sexy" (like the Rubik's cube) -- tries to encourage wide variety theory through cryptography seemed to fall on deaf ears, however being capable of "see" institution idea on the cube became pretty popular.
(Responses specifically welcome from folks who grew up in the percent -- any mathematical subjects you desire were protected within the excessive college curriculum?)