R. D. Sharma Solutions for Chapter: Probability, Exercise 2: EXERCISE 16.2

Suppose you drop a tie at random on the rectangular region shown in the figure. What is the probability that it will land inside the circle with diameter $1 \mathrm{m}$? 

In the accompanying diagram, a fair spinner is placed at the centre $\mathrm{O}$ of the circle. Diameter $\mathrm{A}\mathrm{O}\mathrm{B}$ and radius $\mathrm{O}\mathrm{C}$ divide the circle into three regions labelled $\mathrm{X},\mathrm{}\mathrm{Y}$ and $\mathrm{Z}.$ If $\mathrm{\angle }\mathrm{B}\mathrm{O}\mathrm{C}=45°$. What is the probability that the spinner will land in the region $\mathrm{X}?$

A target shown in the figure consists of three concentric circles of radii $3 \mathrm{cm}, 7 \mathrm{cm}$ and $9 \mathrm{c}\mathrm{m}$ respectively. A dart is thrown and land on the target. What is the probability that the dart will land on the shaded region?

In the figure, points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are the centres of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$. What is the probability that the point will be chosen from the shaded region?

In the figure, $\mathrm{J}\mathrm{K}\mathrm{L}\mathrm{M}$ is a square with sides of length $6 \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}$. Points $\mathrm{A}$ and $\mathrm{B}$ are the midpoints of sides $\mathrm{K}\mathrm{L}$ and $\mathrm{L}\mathrm{M}$, respectively. If a point is selected at random from the interior of the square. What is the probability that the point will be chosen from the interior of $△\mathrm{J}\mathrm{A}\mathrm{B}?$

In the figure dart board is shown. The length of the larger square is $1.5$ times the length of side of the smaller square. If a dart is thrown and lands on the larger square. What is the probability that it will land in the interior of the smaller square?