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Among all the students at a certain high school, the probability of pi

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Among all the students at a certain high school, the probability of pi  [#permalink]

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New post 10 Dec 2019, 02:04
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Among all the students at a certain high school, the probability of picking a left-handed student is \(\frac{1}{4}\), and the probability of picking a student who is learning Spanish is \(\frac{2}{3}\) Which of the following could be the probability of picking a student who is either left-handed or learning Spanish or both?

I. \(\frac{2}{3}\)
II. \(\frac{3}{4}\)
III. \(\frac{5}{6}\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

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Among all the students at a certain high school, the probability of pi  [#permalink]

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New post 10 Dec 2019, 07:56
Bunuel wrote:
Among all the students at a certain high school, the probability of picking a left-handed student is \(\frac{1}{4}\), and the probability of picking a student who is learning Spanish is \(\frac{2}{3}\) Which of the following could be the probability of picking a student who is either left-handed or learning Spanish or both?

I. \(\frac{2}{3}\)
II. \(\frac{3}{4}\)
III. \(\frac{5}{6}\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Are You Up For the Challenge: 700 Level Questions


Use 2 by 2 matrix
Let the total number be 120 as the fractions have denominator 3 and 4
............S........NS
L...........b....... a.....\(120*\frac{1}{4}=30\)
R..........c.........d.... \(90\)
Total.....80......40....\(120\)

Now we are looking at
\(\frac{(a+b+c)}{120}\)
Least value will be when a=0 and b=30 and c=50....\(\frac{80}{120}=\frac{2}{3}\)
Greatest value will be when b=0 and a=30 and c=80...\(\frac{(80+30)}{120}=\frac{11}{12}\)

All the fractions are within this range, so E

Let us test



I. \(\frac{2}{3}\)....b=30, a=0 and c=50
II. \(\frac{3}{4}\).... b=20, a=10 and c=60
III. \(\frac{5}{6}\)...b=10, a=20 and c=70
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Among all the students at a certain high school, the probability of pi  [#permalink]

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New post 15 Dec 2019, 00:28
[quote="Bunuel"]Among all the students at a certain high school, the probability of picking a left-handed student is \(\frac{1}{4}\), and the probability of picking a student who is learning Spanish is \(\frac{2}{3}\) Which of the following could be the probability of picking a student who is either left-handed or learning Spanish or both?

I. \(\frac{2}{3}\)
II. \(\frac{3}{4}\)
III. \(\frac{5}{6}\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Hi Bunuel,

Could you please share the solution?
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Re: Among all the students at a certain high school, the probability of pi  [#permalink]

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New post 15 Dec 2019, 01:51
2
Assume total students = LCM(3,4)=12

\(N(l)= \frac{1}{4}*12=3\)
\(N(s)= \frac{2}{3}*12=8\)

We need the minimum and maximum value of [N(l) U N(s)]

[N(l) U N(s)]= N(l) + N(s) - [N(l) ∩ N(s)]

1. For the maximum value, minimize [N(l) ∩ N(s)].
Minimum possible value of [N(l) ∩ N(s)]=0

[N(l) U N(s)]= N(l) + N(s)-0
[N(l) U N(s)]= 3+8=11

2. For the minimum value, maximize [N(l) ∩ N(s)].
Maximum possible value of [N(l) ∩ N(s)]=3

[N(l) U N(s)]= N(l) + N(s)-3
[N(l) U N(s)]= 3+8-3=8

probability of picking a student who is either left-handed or learning Spanish or both = P

\(\frac{8}{12} ≤ P ≤ \frac{11}{12}\)

All 3 options lie in the range.



Bunuel wrote:
Among all the students at a certain high school, the probability of picking a left-handed student is \(\frac{1}{4}\), and the probability of picking a student who is learning Spanish is \(\frac{2}{3}\) Which of the following could be the probability of picking a student who is either left-handed or learning Spanish or both?

I. \(\frac{2}{3}\)
II. \(\frac{3}{4}\)
III. \(\frac{5}{6}\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Are You Up For the Challenge: 700 Level Questions
GMAT Club Bot
Re: Among all the students at a certain high school, the probability of pi   [#permalink] 15 Dec 2019, 01:51
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