## anonymous one year ago the results of a medical test show that of 32 people selected at random who were given the test, 2 tested positive and 30 tested negative. Determine the odds in favor of a person selected at random testing positive on the test.

1. kropot72

The odds are the ratio of the probability of an event occurring to that of its not occurring. What is the experimental probability of a randomly tested person testing positive?

2. anonymous

you lost me with that last part.

3. kropot72

The experimental probability of a randomly tested person testing positive is given by: $\large \frac{number\ testing\ positive}{total\ number\ tested}$

4. anonymous

so it would be as simple as 2/64?

5. anonymous

then simplify it obviously

6. kropot72

Where did '64' come from?

7. anonymous

crap so it would just be "32" sorry insomnia is setting in!

8. kropot72

Yes, the experimental probability of a randomly tested person testing positive is 2/32. Next step: What is experimental probability of a randomly tested person testing negative?

9. anonymous

so it would be 30/32?

10. anonymous

testing negative.

11. kropot72

Correct. So looking at the definition of odds: 'The odds are the ratio of the probability of an event occurring to that of its not occurring.' So an initial result for the required odds in favor of a person selected at random testing positive on the test is: 2/32 : 30/32 which can be simplified. Can you simplify it?

12. kropot72

The aim is to simplify $\large \frac{2}{32}:\frac{30}{32}$ to get an integer on each side.

13. kropot72

Multiply each term by 32/2

14. kropot72

$\large (\frac{2}{32}\times\frac{32}{2}):(\frac{30}{32}\times\frac{32}{2})=?$

15. anonymous

Sorry I was reading the book and it gave me a weird formula I was trying to wrap my head around based on what we were working on

16. anonymous

it should be 1:15 if I did my math right

17. kropot72

Correct :)

18. anonymous

Theres a formula for odds in favor, the way you just walked out, is that the same process?

19. kropot72

If the probability of an event A occurring is P(A) and the probability of event A not occurring is $\large P(\bar{A})$ then the odds in favor of event A is given by $\large P(A):P(\bar{A})$ This is the method that I used.

20. anonymous

awesome, ok I think I have it. up for helping me with a couple more?

21. kropot72

You're welcome :)

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