Question 1040009: Please help: I believe the answers I put in are correct, but do not understand PART D? Please provide step by step breakdown of how the answers were derived.
Thanks,
Bayes' theorem on conditional probabilities states that, if P(B) is not 0, then
Yesterday car lot Alpha had four Toyotas and one Chevrolet for sale. Car lot Beta had three Toyotas and five Chevrolets for sale. This morning Alan bought a car, choosing one of the two lots at random and then choosing a car at random from that lot.
What is the probability that Alan bought from Alpha? Leave your answer as a fraction in simplest form.
(Fill in the blanks below and give your answers as whole numbers.)
The probability that Alan bought from Alpha is 1/2
If Alan bought from Alpha, what is the probability he bought a Toyota? Leave your answer as a fraction in simplest form.
(Fill in the blanks below and give your answers as whole numbers.)
The probability that he bought a Toyota is 4/5
If Alan bought from Beta, what is the probability he bought a Toyota? Leave your answer as a fraction in simplest form.
(Fill in the blanks below and give your answers as whole numbers.)
The probability that he bought a Toyota is 3/8
It can be shown that the probability that Alan bought a Toyota is 25/48. What is the probability Alan bought from Alpha given that he bought a Toyota? Leave your answer as a fraction in simplest form.
(Fill in the blanks below and give your answers as whole numbers.)
The probability is ?????
Found 2 solutions by solver91311, Boreal:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Bayes Theorem says that the probability of event A given that event B has occurred, ) , is given by the probability of event B given that A has occurred, ) , times the probability of event A, ) , divided by the probability of event B, ) , assuming \ \not=\ 0) .
Assuming event A is that he bought from dealer Alpha, and event B is that he bought a Toyota, then part b of your question (which you did correctly) gives you .
Part a. of your question (which you also did correctly) gives you .
Part d. of your question provides as a given, so:
Plug the numbers into
\ =\ \frac{P(B|A)\,\cdot\,P(A)}{P(B)})
And do the necessary arithmetic.
John
My calculator said it, I believe it, that settles it
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! I agree with a, b, c answers.
I don't agree with the 25/48, using the tree diagram below.
A----------------B
1/2---------------1/2
T----C-----------T-------C
4/5---1/5--------3/8-----5/8
Probability of Toyota is 2/5+3/16=47/80
-------A-----------B--------T
T-----4------------3--------7
C-----1------------5--------6
Tot----5------------8-------13
From the table, if he bought a Toyota, there is a 4/7 chance it came from A.
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