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/sci/ - Science & Math

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2401365 No.2401365 [Reply] [Original]

Hey there /sci/, I've got another question I'm unsure about and the answer doesn't seem correct (there've been many problems with the answers supplied before).

In school where all students take Math and English, 80% of the students pass Math, 93% of the students pass English, and 4% of the students fail both. What percentages of students fail either Math or English or both?

I say it's:
P(math' or english' or english' and math') = P(math' and english) + P(math and english') + P(math' and english')
=0.2 * 0.93 + 0.07 * 0.8 + 0.04 = 0.282

Now, the answer says
P(Fail Math or English) = P(Fail Math) + P(Fail English) – P(Fail Math and English)
P(Fail Math or English) = 0.20 + 0.07 – 0.04 = 0.23

But that's not what the question was asking! it was asking for P(Fail math or english or both), not P(fail math or english).

So, /sci/, which is right? (or are none of them right?)

>> No.2401370

ITT: Pointless Words, Numbers,

>WHAT DO THEY MEAN?

>> No.2401377

20 + 7 - 4 = 19%.

You have to subtract 4% to avoid double-counting that group.

>> No.2401383

4% fail both you are overthinking this

4% failed both
meaning 3% failed english but not math and
16% of the students failed maths but not english

meaning 23% in total failed a subject

>> No.2401406

Your interpretations are equivalent -- although it may not look like this, when the book says "Fail Math or English", it really means "Fail math or english or both" (lrn2mathspeak). Your calculation is off, however:
>P(math' or english' or english' and math') = P(math' and english) + P(math and english') + P(math' and english')
(correct so far)
>=0.2 * 0.93 + 0.07 * 0.8 + 0.04
This is wrong. P(math' and english) <span class="math">\neq[/spoiler] P(math') * P(english) in general; this equivalence only holds when the two events are independent, which they are not.

>> No.2401426

P(Fail math or english or both) = 1 - P(pass both)
I'll let you go from there.

>> No.2401429

>>2401406
So how would I calculate P(math' and english)? Given they're not independent events, I'm assuming it's not possible to do so without more information?

>>2401383
Thanks for that interpretation, it makes sense

>> No.2401440

>>2401426
As >>2401406 pointed out the two events aren't independent so calculation P(pass both) isn't very easy