SOLUTION: Suppose the probability of an IRS audit is 1.2 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more. (a) What are the odds that such a taxpayer will be

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose the probability of an IRS audit is 1.2 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more. (a) What are the odds that such a taxpayer will be       Log On


   

Question 1150394: Suppose the probability of an IRS audit is 1.2 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.
(a) What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)
Odds that a taxpayer will be audited
.88
to

(b) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)
Odds against a taxpayer being audited
to
i cant get past the first answer i got can you please help me im racking my brain
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your answer to the first part is incorrect.

odds in favor = probability (for) / probability (against)

odds against = probability (against) / probability (for)

another way of saying this is:

odds in favor = (number of ways for) / (number of ways against)

odds against = (number of ways against) / (number of ways for).

based on your problem:

if the probability for is 1.2%, then the probability against is 98.8%.

note that the probability against is equal to 100% minus the probability for.

that's 100% minus 1.2% = 98.8%.

the odds for are therefore 1.2% / 98.8% = 1.2 to 98.8.

that can be shown as 1.2 / 98.8.

multiply both numerator and denominator by 3 / 1.2 and you get:

1.2 / 98.8 is equivalent to 3 / 247.

the odds in favor are 3 to 247 when you are looking for the numerator and the denominator to both be integers.

probability (for) is equal to odds (for) divided by (odds (for) + odds (against)).

probability (for) is therefore 3 / 250 = .012 * 100 = 1.2%.

that's what we started with, so the numbers are correct.

the odds against would be 98.8% / 1.2% = 98.8 to 1.2.

that can be shown as 98.8 / 1.2.

multiply both numerator and denominator by 3 / 1.2 and you get:

247 / 3.

the odds against are 247 to 3 when you are looking for the numerator and the denominator to both be integers.

probability (aginst) is equal to odds (against) divided by (odds (for) + odds (against)).

probability (against) is therefore 247 / 250 = .988 * 100 = 98.8%.

that's what we started with, so the numbers are correct.

the second way to explain odds in favor and odds against is:

odds in favor = (number of ways for) / (number of ways against)

odds against = (number of ways against) / (number of ways for).

assume you have 1000 possible occurrences.

assume 12 possible way to get the desired outcome and 988 possible ways to not get the desired outcome.

probability (for) is therefore 12 / 1000 = .012 = 1.2%.
probability (against) is therefore 988 / 1000 = .988 = 98.8%

odds for is 12 / 988 * (1/4) / (1/4) = 3 / 247.

odds against is 988 / 12 * (1/4) / (1/4) = 247 / 3.

same odds and probabilities are calculated either way.

here's some references you might find instructive.

https://www.mathplanet.com/education/pre-algebra/probability-and-statistic/finding-the-odds

https://www.mathplanet.com/education/pre-algebra/probability-and-statistic/probability-of-events

https://stats.seandolinar.com/statistics-probability-vs-odds/