Answer:
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
