1. ## Bayesian and Probability

A certain disease has infected 2% of the population. The firm has annoucned that 90% of those infected will show a postive test result , while 95% of those not infected will show a negative test result. Infected should show positive and non-infected negative. The proportion of correct test results is?

Ans:0.949

How do I solve this??

2. Swetha has applied for a job with company A and Company B.She feels she has a 50% chance of receiving offer from company A and 15% chance from company B. If she receives from company B , she has an 80% chance of receiving from company A.

The probability that at least one company will make an offer to her is?

Ans:65%

I tried but really couldn't get the answer

thanks

2. ## Re: Bayesian and Probability

Hope the test went well.

Question #1, Prevalence = 2%, Sensitivity = 90%, Specificity = 95% => plug numbers into a 2x2 classification table and divide a+c / a + b + c + d (a is cell 1,1; b = 1,2; c 2,1; d = 2,2)

3. ## Re: Bayesian and Probability

#2, I am not so good at these conditional questions, however the question says at least one job. So I believe you can ignore the 80% part of the content. Thus it may be as simple as 50% + 15%?

4. ## Re: Bayesian and Probability

Originally Posted by hlsmith
Thus it may be as simple as 50% + 15%?

It isn't. The only way that would work is if you could never receive an offer from both companies. But building the 2x2 table would be a good idea in this case as well. You're given all the marginal probabilities and from the conditional statement you can figure out one of the cells which will allow you fill in the rest of the cells and then you can use that to find the answer.

Also I think the given answer is wrong.

5. ## The Following User Says Thank You to Dason For This Useful Post:

hlsmith (03-18-2015)

6. ## Re: Bayesian and Probability

Yeah, I figured that reply was too easy. I can't decide if I care enough, but I guess since you said a table could be used and I can't visualize that - I will inquire on how to correctly answer the second problem.

7. ## Re: Bayesian and Probability

The information we know is given below. We can solve for X based on the statement about the conditional probability we were given. Once we know X we can fill out the rest of the cells as described in the table.

8. ## Re: Bayesian and Probability

Yeah, I had gotten the marginals, but the rest is confusing for me. Especially if cell "C" is 0.15 - 0.40 = -0.25. How can the cell value be a negative??

9. ## Re: Bayesian and Probability

Originally Posted by hlsmith
Yeah, I had gotten the marginals, but the rest is confusing for me. Especially if cell "C" is 0.15 - 0.40 = -0.25. How can the cell value be a negative??
How are you getting X to be .40? Note that the conditional we are given is the probability of A being yes given that B is yes. This is different than the probability of B being yes given that A is yes.

10. ## Re: Bayesian and Probability

No idea how I got 40%? You can input any number in for X and get it to work - however we are presented with .8 in the problem.

I am lost on this one, since it is conditional but as you point out A|B not same as B|A.

11. ## Re: Bayesian and Probability

Ah yeah but X is P(A is yes AND B is yes). We aren't given that probability directly but we are given P(B is yes) and P(A is yes | B is yes). A probability law tells us that P(A AND B) = P(A|B)*P(B) so X = P(A is yes AND B is yes) = P(A is yes | B is yes)*P(B is yes) = .8*.15

12. ## Re: Bayesian and Probability

Just plug in the numbers, hot shot! Illuminate this myopic being.

13. ## Re: Bayesian and Probability

You want me to finish the problem? I pretty much never do that! But I already gave you the numbers - now all you need to do is plug them in

14. ## Re: Bayesian and Probability

I hate your kind. Funny enough I got the same answer that I originally came to before posting. Is it an integer that is > 52 and < 54, then subsequently multiplied by .01?

16. ## Re: Bayesian and Probability

Originally Posted by Dason

Thanks.

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