Question

are even, r even. A 1.1-14·Let the interval [-r,r] be the base of a semicircle. ne of the f a pot is selected at random from this interval, assign abilty of a probability to the event that the length of the perpen- e slot into dicular segment from the point to the semicircle is less than r/2. 1.1-15. Let S = A1 U A2 U U Am, where events (a) If P(A1) P(A2)P(A), show that P(Ai - (b) If A A1 UA2U..UAh, where h<m, and (a) holds, A1, A2,Am are mutually exclusive and exhaustive. randomly Use your prove that P(A) h/m

Answer 1

1.1-14)

The height of the perpendicular is given by $H=\sqrt {r^2 - x^2}$ ​​​​​​, where X denotes the base of simicircle.

Then required probability is