Question 16 - End-of-Chapter Exercises - Chapter 7 - The Mathematics of Maybe: Introduction to Probability

Transcript

Question 16 Suppose you drop a dye at random on the rectangular region shown in Fig. 7.8. What is the probability that it will land inside the circle with a diameter of 1 m? Here, we use area to find probability Now, Probability it will land inside circle of diameter 1 m = (𝑨𝒓𝒆𝒂 𝒐𝒇 𝒄𝒊𝒓𝒄𝒍𝒆 𝒘𝒊𝒕𝒉 𝑫𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝟏 𝒎)/(𝑻𝒐𝒕𝒂𝒍 𝒂𝒓𝒆𝒂) Let’s find them individually Area of circle with Diameter 1 m Now, Diameter of circle = 1 m Radius of circle = 1/2 m Now, Area of circle = πr2 = π(1/2)^2 = π ×𝟏/𝟒 m2 Total Area Total Area is a a rectangle with Length = 3 m Breadth = 2 m Now, Area of rectangle = Length × Breadth = 3 × 2 = 6 m2 Now, P (die will land inside circle) = (𝐴𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒)/(𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎) = (𝜋 × 1/4)/6 = 𝜋/(6 × 4) = 𝝅/𝟐𝟒 So, Probability is 𝝅/𝟐𝟒