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Probability
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Section:
Mathematics
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© examsnet.com
Question : 1
Total: 92
An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3 . The device gives accurate result in 8 out of 10 such tests. If the device reports that an item tested is not defective, then the probability that it is actually defective is
[AP EAPCET 24 May 2025 S1]
‌
‌
2
15
‌
‌
3
29
‌
‌
3
31
‌
‌
4
51
Validate
Solution:
Let
D
be the event that an item is defective, and
N
be the event that an item is not defective.
So,
P
(
D
)
=
0.3
and
P
(
N
)
=
1
−
0.3
=
0.7
Probability of an accurate result
=
‌
8
10
=
0.8
=
P
(
R
D
∕
D
)
Probability of an inaccurate result
=
1
−
0.8
=
0.2
=
P
(
R
N
∕
D
)
So,
P
(
D
∩
R
N
)
=
P
(
R
N
∕
D
)
×
P
(
D
)
=
0.2
×
0.3
=
0.06
P
(
N
∩
R
N
)
‌
=
P
(
R
N
∕
N
)
×
P
(
N
)
‌
=
0.8
×
0.7
=
0.56
0
,
P
(
R
N
)
‌
=
P
(
D
∩
R
N
)
+
P
(
N
∩
R
N
)
‌
=
0.06
+
0.56
=
0.62
P
(
D
∕
R
N
)
‌
=
‌
P
(
D
∩
R
N
)
P
(
R
N
)
=
‌
0.06
0.62
=
‌
6
62
=
‌
3
31
∴ The probability of an item is actually defective given device reports it as not defective is
‌
3
31
.
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