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N
=
16
N = 16
N
=
16
items with
M
=
1
M = 1
M
=
1
marked item uses rotation angle
θ
=
arcsin
(
1
/
16
)
\theta = \arcsin(\sqrt{1/16})
θ
=
arcsin
(
1/16
)
. After the optimal
r
=
r
o
u
n
d
(
π
/
(
4
θ
)
−
1
/
2
)
=
3
r = \mathrm{round}(\pi/(4\theta) - 1/2) = 3
r
=
round
(
π
/
(
4
θ
)
−
1/2
)
=
3
iterations, the success probability is
sin
2
(
(
2
r
+
1
)
θ
)
\sin^2((2r+1)\theta)
sin
2
((
2
r
+
1
)
θ
)
. What is this probability?
0.0625
0.961
0.582
0.908
Check answer