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Byju's Answer
Standard XII
Mathematics
Combination
An integer is...
Question
An integer is chosen at random between
1
and
100
. The probability that it is divisible by
8
is
m
25
. Find
m
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Solution
Number of integers between
1
and
100
are
100
.
Clearly, this is the size of the sample space also.
The first integer between
1
and
100
divisible by
8
is
8
and the last integer in the same range divisible by
8
is
96
.
So, these numbers form an A.P. with first term
8
and common difference
8
.
So, we have
a
n
=
96
,
a
1
=
d
=
8
⇒
n
−
1
=
a
n
−
a
1
d
=
96
−
8
8
=
11
⇒
n
=
11
+
1
=
12
.
So there are
12
integers between
1
and
100
that are divisible by
8
and each number is equally likely of being picked.
So the probability that a randomly chosen integer in the given range is divisible by
8
is
12
100
=
3
25
.
hence
m
=
3
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An integer is chosen at random between
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.
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