Question

Suppose that you toss a dart at a circular target of radius 10 inches. Given that the dart lands in the lower half of the target, find the probability that

1. its distance from the center is greater than 3 inches.

II it lands within 3 inches of the point (0, −3).

Answer 1

1)here total area of lower half P(LH)=(pi/2)*r² =(pi/2)*10² =(pi/2)*100

area of lower half greater than 3 inches from center =(pi/2)*(10²-3²) =(pi/2)*(91)

hence P( distance from the center is greater than 3 inches given lands in the lower half of the target)

=(pi/2)*(91)/(pi/2)*100 =91/100 =0.91

2)

area of lower left half till distance -3 =(pi)*3² =(pi)*(9)

hence P(  lands within 3 inches of the point (0, −3) given lands in the lower half of the target)

=(pi)*(9)/(pi/2)*100 =9/50=0.18