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Particle in a box ground states

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The ground state wave function for a particle in a box confined to a 1-D box of length L is &#936;=(2/L)^(1/2) sin (pi x/ L)
Suppose that the box is 10.0 nm long. Calculate the probability that the particle is
a) between x=9.90 nm and x= 10.0 nm
b) in the right half of the box

https://brainmass.com/physics/wavefunction/particle-box-ground-states-302022

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(1.1)
Therefore:
(1.2)
The probability to find the particle between and is given by:
(1.3)
For the ground state:
(1.4)
Therefore:
(1.5)
Simple substitution:
(1.6)
And we get normalization of the box width (we set L=1) and the interval is now measured in the fraction of the box's size
(1.7)

For we obtain the probability:

For we obtain the probability:

As expected, due to the symmetry of the ground state the particle has 50% to be in the right 50% of the box.

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