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Bunuel
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Step 1: Define variables
Let N be the total number of students.
Let X be the number of students who receive exactly one pencil.
Let Y be the number of students who receive at least two pencils.

Step 2: Translate given statements

(1) 110 students are expected to get at least one pencil.
- This means N = 110.

(2) 60 students are expected to get at least two pencils.
- This means Y = 60.

Step 3: Find X
Since every student gets at least one pencil, the number of students who get exactly one pencil is:
X = N - Y
X = 110 - 60
X = 50

Step 4: Compute probability
The probability that a randomly chosen student gets exactly one pencil is:
P(X) = X / N = 50 / 110 = 5/11

Final Answer: 5/11
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To find: probability that a student gets exactly one pencil in the exam hall

(1) 110 students are expected to get at least one pencil...
Students getting 1 or more than 1 pencil= 110
Insufficient

(2) 60 students are expected to get at least two pencils...
Students getting 2 or more pencils= 60
Insufficient

Taking (1)&(2) together
Students getting exactly 1 pencil= (Students getting 1 or more than 1 pencil)-(Students getting 2 or more than 2 pencils)
= (110)-(60)= 50

Probability= 50/110= 5/11

Answer: C
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If each student gets at least one pencil in the exam hall, then Total number of students is same as students who get atleast one pencil
\(P = \frac{{Student gets exactly 1 Pencil}}{{All students} }\) OR \(\frac{{Student gets exactly 1 Pencil}}{{Students get atleast one pencil} }\)

Statement 1
Given 110 students are expected to get at least one pencil, All students = 110
\(P = \frac{{Student gets exactly 1 Pencil}}{{All students} }\)
\(P = \frac{{Student gets exactly 1 Pencil}}{110 }\)
We don't know the numerator
Insufficient

Statement 2
Given 60 students are expected to get at least two pencils
We don't know anything about students who gets exactly one pencil
Insufficient

Combined, we have students who get at least one pencil = 110 and students who get at least two pencil = 60.
This means exactly students who get exactly one pencil = 110-60 = 50
Using 1, we know
\(P = \frac{{Student gets exactly 1 Pencil}}{110 }\)
P = 50/110
Answer C
Bunuel
If each student gets at least one pencil in the exam hall, what is the probability that a student gets exactly one pencil in the exam hall?

(1) 110 students are expected to get at least one pencil.
(2) 60 students are expected to get at least two pencils.


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