Probability question

Question

The probability of a student entering college and not needing developmental math or English courses is 55%. The probability that the student will need only developmental math is 31% and the probability the student will need only English is 31%.

 

What is the probability the student will need both developmental math and English? 

Answer 1

Hello Landon T.,

Since P(NoNeeds)=55%, then P(SomeNeeds)=45%. If you remove the isolated populations P(needsOnlyEnglish)=31% and P(needsOnlyMath)=31%, then P(needsBothMathand English)=0.45-(0.31+0.31) = -0.17. Since probabilities can't be negative, right away there's a problem with English, either yours in transcribing the problem or your instructor's in proposing an impossible set of conditions. And if you didn't arrive at the same conclusion, probably you need the math.(?). This situation is called 'Irony" in language analysis.

Now, if the 31%'s had been "needsAt LeastMath" and "needsAt LeastEnglish", then you could have had +0.17 overlap=NeedsBothMathandEnglish, and needsMathOnly and needsEnglishOnly would be 0.14 each -- this value totals with 0.17 to give the 0.31's stated.

--Cheers, --Mr. d.