Let P = (x, y) be a point chosen at random in the unit disc, centre (0, 0) and radius 1. Describe...

Question

Let P = (x, y) be a point chosen at random in the unit disc, centre (0, 0) and radius 1. Describe the model of this experiment, and

evaluate the probabilities that P is within 0.5 of the centre; that

y > 1/

√2; and that both |x − y| <>

Aditi · Accepted Answer

ANSWER 
a. P is within 0.5 of the center.
Total radius of disc = π(1)2 = π
Area of the portion of the disc 0.5 from the center = π(0.5)2 = 0.25 π
P(distance of point within 0.5 of the center ) = A 0.5   = 0.

Let P = (x, y) be a point chosen at random in the unit disc, centre (0, 0) and radius 1. Describe the model of this experiment, and evaluate the probabilities that P is within 0.5 of the centre; that...

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