# Suppose you drop a die at random on the rectangular region shown in Fig. 15.6. What is the probability that it will land inside the circle with diameter 1m?

**Solution:**

We use the concepts of areas of circles and squares and also the basic concepts of probability.

Length of rectangular region = 3 m

Breadth of rectangular region = 2 m

Area of rectangular region = Length × Breadth

= 3 × 2

= 6 m²

Diameter of circular region = 1 m

Radius of circular region = 1/2 m

Area of circular region = πr²

= π × (1/2)²

= π/4

The probability that it will land inside the circle = Number of possible outcomes/Total number of favourable outcomes

= Area of circular region/Area of the rectangular region

= (π/4)/6

= π/24

The probability that it will land inside the circle is π/24.

Check out more in terms of probability

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 15

**Video Solution:**

## Suppose you drop a die at random on the rectangular region shown in Fig. 15.6. What is the probability that it will land inside the circle with diameter 1m?

NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 20

**Summary:**

If suppose you drop a die at random on the rectangular region shown in figure, then the probability that it will land inside the circle with a diameter of 1 m is π/24.

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