Question

Consider the Cartesian plane R² and Let X denote the subset of points for which both coordinate are integer. A coin of diameter 1/2 is tossed randomly onto the plane. The probability p that the coin covers a point of X -

• A. 0.2
• B. 0.8
• C. 1.2
• D. None of these

Answer 1

Answer: (A)

0.2

Answer 2

Let S denote the set of points inside a square with corner

(a, b), (a, b + 1), (a + 1, b), (a + 1, b + 1) Ī X.

Let P denotes the set of points in S with distance less than 1/4 from any corner point. Thus A coin whose centre falls in S will cover a point of X if and only if its centre falls in a point of P

P = = $\frac { \pi ( 1 / 4 ) ^ { 2 } } { 1 }$ = $\frac { \pi } { 16 }$ » 0.2