Asifpirlo wrote:

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

st1 implies there are 110 students in the exam hall and everyone of them will get exactly one pencil.

but its not sufficient.

st2 tells, 60 students are expected to get at least two pencils. this not sufficient alone.

Now from both statements,

110 = exactly one + more than one

or 110 = exactly one + 60

or, exactly one = 50 .

so the probability of getting exactly one = 50/110 = 5/11 ,

so Answer (C)

Each student gets one pencil . and 110 students got one pencil. There are 110 students in the exam hall.

Statement A:- 110 students gets atleast one pencil in the exam hall. With this we can only get the number of students in the exam hall.But not the number of students who got exactly one pencil. So A and D are out

Statement B:- 60 students are expected to get atleast two pencils in the exam hall. With this statement ALONE we will not be able to get the number of students who got exactly two pencils in the exam hall. So B is out.

Both statements combined. we get that 110 students get atleast one pencil. and 60 students get atleast two pencils. Refer to the diagram below

Attachment:

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So the number of students who got exactly one pencil is the middle portion. ie 110 - 60 = 50. So the answer is C