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# Of the 100 students at a certain school, 30 students are

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Joined: 31 Dec 1969
Location: India
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Of the 100 students at a certain school, 30 students are [#permalink]  02 Sep 2004, 15:13
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Of the 100 students at a certain school, 30 students are taking a chemistry class, 40 students are taking a physics class, and 20 students are taking both a physics and a chemistry class. If a student is chosen at random from the school, what is the probability that he or she is taking a physics or a chemistry class?

A) 1/2
B) 3/10
C) 5/12
D) 3/5
E) 1/4
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With Venn Diagram, you have:
10 only chemistry
20 only physics
20 chemistry&physics

Odds are 1/2 of students will be taking either physics or chemistry
A it is
_________________

Best Regards,

Paul

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20 physics only
20 physics and chemistry
10 chemistry only

Let event A - students taking physics
event B - students taking chemistry

P(AUB) = P(A)+P(B) - P(A interesect B) --> Not mutually exclusive since both event A and B can happen together

= 20/100 + 10/100 - 20/100
= 1/10
Manager
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Wilfred... you have used the right formula but your set-up is wrong:

P(AUB) = P(A) + P(B) - P(A intersect B) where P(A) is the probability of event A and NOT event A only.

so it should be:

A: students taking Physics: P(A) = 4/10
B: Students taking Chem: P(B) = 3/10

So, P (AUB) = P(A) + P(B) - P(A intersect B)
= (4+3-2)/10
= 1/2 ( as Paul suggested and albeit much quicker to use his method)
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Thanks drdas ! I was wondering whether to use event A only or event A as a whole. You answered my doubts. Thanks once more !
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Paul wrote:
With Venn Diagram, you have:
10 only chemistry
20 only physics
20 chemistry&physics

Odds are 1/2 of students will be taking either physics or chemistry
A it is

Paul, isn't the question asking for "probability that he or she is taking a physics or a chemistry class" and you answered for "probability that he or she is taking a physics or a chemistry class or both"

I think it might be 10+20/100 = 3/10 (Choice B)
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hardworker, there are students taking physics only, chemistry only, and students taking both subjects.

If you pick a student and he/she (bad english here, don't use he/she for verbal !) is taking either physics or chemistry, that student can belong to anyone group. We need to ask are the two events mutually exclusive ? Yes. Because there are students who do both subjecs.

So the way to do this is P(A) + P(B) - P(A intersect B)
Joined: 31 Dec 1969
Location: India
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GMAT 2: 740 Q40 V50
GMAT 3: 700 Q48 V38
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GPA: 3.31
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here its said only chemistry and only physics

10/100 + 20/100 = 30/100 = 3/10

Please correct me , i think we cannot use the sets formula of
P(AUB) here .

we took the approach of venn diagram to solve this problem but this is not a "SETS " problem .

if we negate also it should be then
40/100 + 30/100 - 20/100 -20/100 = 30/100
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What I understand from the question stem is that he or she is taking a physics class or a chemistry class. The underlying assumption here is a student cannot be taking both class simultaneously.

Shouldn't the universe of these Physics and chemistry students be what Paul had worked out?
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