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18 February, 08:50

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?

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  1. 18 February, 10:32
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    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
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