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    Geometric Probability

    Uploaded by

    Romeo Jr Pacheco Opena
    - Probability is calculated by taking the length/area of the event space and dividing it by the total length/area of the sample space. - In a line segment between points A and B, the probability of a randomly selected point being between two other points C and D is the length of segment CD divided by the total length AB. - In a square, the probability of a randomly selected point being inside a triangle within the square is 1/2. - In a circle inside a square, the probability of a dart randomly landing in the circle is approximately 0.785.

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    Geometric Probability

    Uploaded by

    Romeo Jr Pacheco Opena
    146 views8 pages
    - Probability is calculated by taking the length/area of the event space and dividing it by the total length/area of the sample space. - In a line segment between points A and B, the probability of a randomly selected point being between two other points C and D is the length of segment CD divided by the total length AB. - In a square, the probability of a randomly selected point being inside a triangle within the square is 1/2. - In a circle inside a square, the probability of a dart randomly landing in the circle is approximately 0.785.

    Original Description:

    Geometric Probability

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    © © All Rights Reserved

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    - Probability is calculated by taking the length/area of the event space and dividing it by the total length/area of the sample space. - In a line segment between points A and B, the probability of a randomly selected point being between two other points C and D is the length of segment CD divided by the total length AB. - In a square, the probability of a randomly selected point being inside a triangle within the square is 1/2. - In a circle inside a square, the probability of a dart randomly landing in the circle is approximately 0.785.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    146 views8 pages

    Geometric Probability

    Uploaded by

    Romeo Jr Pacheco Opena
    - Probability is calculated by taking the length/area of the event space and dividing it by the total length/area of the sample space. - In a line segment between points A and B, the probability of a randomly selected point being between two other points C and D is the length of segment CD divided by the total length AB. - In a square, the probability of a randomly selected point being inside a triangle within the square is 1/2. - In a circle inside a square, the probability of a dart randomly landing in the circle is approximately 0.785.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 8
    At a glance
    Powered by AI
    The key takeaways are that probability is calculated as the ratio of favorable outcomes to total possible outcomes, and examples are given of calculating probabilities for points chosen randomly within geometric shapes and on line segments.

    The answer is 1/2, as the triangle takes up half the area of the square.

    The answer is given as 0.785, as the area of the circle is 0.785 times the area of the enclosing square.

    - is a probability which uses lengths of segments or

    areas of geometric figures


    P(E) = length of segment P(E) = area of the figure
    total length total area

    Example:
    Point on the line segment is chosen at random, what is the
    probability that it is between 25 and 35? Ans 2/5
    A B C D E F

    15 20 25 30 35 40
    Example:
    ACDE is a square. A side of the square is 10cm long.
    B is the midpoint of AC. If a point is chosen at
    random in the square, what is the probability that it
    lies inside triangle EBD? Ans. 1/2
    • A B C

    •
    • 10

    E D
    Example:
    A circle with a diameter of 30 cm is placed inside a
    square whose side is 30-cm long. What is the
    probability that a dart thrown will land inside the
    circle? Ans. 0.785

    • 30
    • Extra Exercise:
    • A point on AG is chosen at random. What is the
    probability that it is on the given segment?

    • A B C D E F G
    •
    • 0 1 2 3 4 5 6

    • 1. BC 3. CD
    • 2. CF 4. BG
    • Find the probability that a point P chosen from AL, is
    on the given segment.

    A B C D E F G H I J K L

    20 25 30 35 40 45 50 55 60 65 70 75

    5. BE 6. CH
    7. EG 8. DK
    • Find the probability that a point selected randomly in
    this figure lies in the shaded region.
    • 8 cm

    6 cm
    • 9. 10. 8 cm

    • 11. 15 cm 12. 10 cm

    • 15 cm 6 cm
    • A dart is thrown at random at the dartboard. The
    radius of the bull’s eye is 2cm, the radius of the
    unshaded circle is 5cm, and that of the outer circle is
    10 cm. Calculate the probability that the dart will hit
    the (a) bull’s eye (b) unshaded region

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