SOLUTION: Suppose the probability of an IRS audit is 5.2 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more. What are the odds that such a taxpayer will be audi

Question 1185121: Suppose the probability of an IRS audit is 5.2 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.
What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)
What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!

odds for = probability for / probability against.
odds against = probability against / probability for.

example;

if probability of an event is .25, then:

odds for = .25 / .75 = 1/3.
odds against = .75 / .25 = 3/1.

and:

probability of winning is .25 / (.25 + .75) = .25 / 1 = 1/4.
probability of losing is .75 / (.25 + .75) = .75 / 1 = 3/4.

if the probability of an event occurring is .052, then:
the probability of that event not occurring is 1 - .052 = .948.

the odds of that event occurring is .052 / .948.

the odds against that event occurring is .948 / .052.

in whole numbers, these ratios becomes:

odds for = 52 / 948
odds against = 948 / 52

these ratios can be simplified to:

odds for = 13 / 237
odds against = 237 / 13

probability for = 13 / (237 + 13) = 13 / 250 = .052
probability against = 237 / (13 + 237) = 237 / 250 = .948

you take .052 / .948 and multiply both sides by 1000 aqnd you get 52 / 948.
that's where the whole numbers come from.

here's a reference on odds versus probabilities.

https://www.thoughtco.com/how-are-odds-related-to-probability-3126553

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