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.

Question

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.

kropot72 · Answer

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?

anonymous · Answer

you lost me with that last part.

kropot72 · Answer

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

anonymous · Answer

so it would be as simple as 2/64?

anonymous · Answer

then simplify it obviously

kropot72 · Answer

Where did '64' come from?

anonymous · Answer

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

kropot72 · Answer

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?

anonymous · Answer

so it would be 30/32?

anonymous · Answer

testing negative.

kropot72 · Answer

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?

kropot72 · Answer

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

kropot72 · Answer

Multiply each term by 32/2

kropot72 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

kropot72 · Answer

Correct :)

anonymous · Answer

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

kropot72 · Answer

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.

anonymous · Answer

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

kropot72 · Answer

You're welcome :)