A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square centimeters. A dart is randomly thrown at the dartboard.

Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle?

The probability that the dart lands inside the triangle is 0.25

Step-by-step explanation:

* Lets explain how to find the probability of an event

- The probability of an Event = Number of favorable outcomes : Total

number of possible outcomes

- P (A) = n (E) : n (S), where

# P (A) means finding the probability of an event A

# n (E) means the number of favorable outcomes of an event

# n (S) means set of all possible outcomes of an event

- P (A) < 1

* Lets solve the problem

- A rectangular dartboard has an area of 648 cm²

- The triangular part of the dartboard has an area of 162 cm²

- A dart is randomly thrown at the dartboard

- The dart lands in the rectangle

∴ The area of the rectangle is the set of all possible outcomes n (S)

- The probability P (A) that the dart lands inside the triangle

∴ The area of the triangle is set of favorable outcomes of an

event n (E)

∵ P (A) = n (E) : n (S)

∴ P (T) = area of the triangle : area of the rectangle

∵ Area of the rectangle is 648 cm²

∴ n (S) = 648

∵ The area of the triangle is 162 cm²

∴ n (E) = 162

∴ P (T) = 162 : 648 = 1/4 = 0.25

* The probability that the dart lands inside the triangle is 0.25