MU DIVISION

Question 48

Probability★★★Question Bank

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Question

Jayden is standing on the point

(0,3)

, and wishes to shine a laser at a random point on an infinite wall located along the

x

-axis. To do this, he chooses an angle

\theta

uniformly at random from the interval

(-\pi/2,\pi/2)

, and positions his laser so it makes an angle of

\theta

with the

y

-axis (positive values of

\theta

point towards the positive

x

-axis). If

X

is the

x

-coordinate of the point on the wall he shines his laser towards, find the probability that

|X|<\sqrt3

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