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from a set of 100 cards numbered 1 to 100 one card
Question:
From a set of 100 cards numbered 1 to 100, one card is drawn at random. Find the probability that the number obtained on the card is divisible by 6 or 8, but not by 24.
WBJEE
Updated On:
Aug 27, 2025
(A)
6
25
(B)
1
4
(C)
1
6
(D)
2
5
Show Solution
Verified By Collegedunia
The Correct Option is
A
Solution and Explanation
Explanation:
E
=
set
of numbers divisible by 6
=
{
6
,
12
,
18
,
24
,
30
,
…
,
96
}
F
=
set
of numbers divisible by
8
=
{
8
,
16
,
24
,
…
,
96
}
E
∩
F
=
set
of numbers divisible by 6 and 8
=
{
24
,
48
,
72
,
96
}
∴
n
(
E
)
=
16
,
n
(
F
)
=
12
,
n
(
E
∩
F
)
=
4
∴
n
(
E
∪
F
)
=
n
(
E
)
+
n
(
F
)
−
n
(
E
∩
F
)
=
16
+
12
−
4
=
24
and
n
(
S
)
=
100
∴
Required probability
=
n
(
E
∪
F
)
n
(
S
)
=
24
100
=
6
25
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