SOLUTION: An IRS auditor randomly selects 2 tax returns (without replacement) from 48 returns of which 9 contain errors. ROUND TO 4 DECIMAL PLACES. PART 1: WHAT IS THE PROBABILITY THAT SH

Question 1195382: An IRS auditor randomly selects 2 tax returns (without replacement) from 48 returns of which 9 contain errors. ROUND TO 4 DECIMAL PLACES.
PART 1: WHAT IS THE PROBABILITY THAT SHE SELECTS EXACTLY ONE HAS AN ERROR AND EXACTLY ONE WITHOUT AN ERROR? (ITS NOT 0.1556)
PART 2: WHAT IS THE PROBABILITY TAHT SHE SELECTS AT LEAST ONE WITH AN ERROR?
(ITS NOT 0.8444)
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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An IRS auditor randomly selects 2 tax returns (without replacement) from 48 returns of which 9 contain errors.
ROUND TO 4 DECIMAL PLACES.
PART 1: WHAT IS THE PROBABILITY THAT SHE SELECTS EXACTLY ONE HAS AN ERROR AND EXACTLY ONE WITHOUT AN ERROR?
(ITS NOT 0.1556)
PART 2: WHAT IS THE PROBABILITY TAHT SHE SELECTS AT LEAST ONE WITH AN ERROR?
(ITS NOT 0.8444)
~~~~~~~~~~~~~~~~~~~~~~

PART 1: THE PROBABILITY THAT SHE SELECTS EXACTLY ONE HAS AN ERROR AND EXACTLY ONE WITHOUT AN ERROR is

        P = P(1-st is ERROR, 2-nd is not ERROR) + P(1-st is not ERROR, 2-nd is ERROR) = 

          =  =  =  = 0.311170213 = 0.3112 (rounded as requested).




PART 2: WHAT IS THE PROBABILITY TAHT SHE SELECTS AT LEAST ONE WITH AN ERROR is

        P = 1 - probability that she selected both with no error

          = 1 -  =  = 0.325797872 = 0.3258 (rounded as requested).




The formulas in the solution are SELF-EXPLANATORY.


48-9 = 39 is the number of tax returns with NO ERROR.

Solved and explained.

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