Question 1194458: How do I calculate probability if I only have a percent and I unsure of the number of taxpayers who earned $100,000 or more?
Suppose the probability of an IRS audit is 2.6 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___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___
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the statement says:
suppose the probability of an IRS audit is 2.6 percent for U.S. taxpayers who file form 1040 and who earned 100,000 or more.
the statement is not asking you to determine the number of taxpayers who earned 100,000 or more.
it is simply telling you that the probability is 2.6% that those people will be audited.
no matter how small or large the group, past experience has indicated that approximately 2.6% of them will be audited.
the determination of how small or large the group is doesn't matter.
whatever the size of the group is, historical records indicate that 2.6% of them are audited.
that means that the probability of any future group that possesses those characteristics (file a 1040 and earn more than 100,000 a year) is also 2.6%.
that, i believe, is called empirical probability.
it's probability based on historical evidence.
the question is not concerned with that.
it is concerned with determining odds that a taxpayer in that group will be audited or not audited.
odds for equals probability that something will occur divided by probability that something will not occur.
odds against equals probability that something will not occur divided by probability that something will occur.
in this problem, the probability that an audit will occur is 2.6%.
the probability that an audit will not occur is therefore 100% minus 2.6% = 97.4%.
the odds that the taxpayer in that group will be audited is therefore 2.6% / 97.4%, or 2.6 / 97.4 = .0266940454 = 13/487.
the odds that the taxpayer in that group will not be audited is therefore 97.4% / 2.6% = 97.4 / 2.6 = 37.46253846 = 487/13.
i used the calculator to get these reduced fractions.
without that, i would just say the odds for are 2.6/97.4 and the odds against are 97.4/2.6.
empirical probability is based on experience.
if you flip a coin many times and the coin comes up heads 25% of the time and the coin comes up tails 75% of the time, then the probability becomes .25 to get heads and .75 to get tails.
the odds of getting heads becomes .25 / .75.
the odds of not getting heads becomes .75 / .25
probability is defined as the number of ways an event can occur divided by the total number of ways.
odds are defined as the number of ways an event can occur divided by the number of ways it cannot 0ccur.
in your problem, experience has shown that taxpayers who file a 1040 and make more than 100,000, are audited 2.6% of the time.
the probability they will get audited is therefore 2.6/100 = .026.
the probability they won't get audited is therefore (1 - 2.6) / 100 = 97.4/100 = .974.
the odds that they will get audited is 2.6/97.4, or .026/.974.
the odda that they will not get audited is 97.4/2.6 = .974/.026.
hope this helps.
let me know if you have any questions.
theo
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