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Probability Concepts

Grade 7 · Statistics · Worksheet 2

  1. P(drawing a card numbered with a multiple of 11 from a bag containing cards numbered 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220) = ? Answer: ______________
  2. P(rolling a 1, 3, or 5 on a fair six-sided die) = ? Answer: ______________
  3. P(drawing a card numbered with an odd number from a bag containing cards numbered 1, 3, 5, 7, 9, 11, 13, 15, 17, 19) = ? Answer: ______________
  4. P(rolling a 3 on a fair six-sided die) = ? Answer: ______________
  5. Hana is creating a large square mural for a community art project. The square mural has a side length of 120 cm. In the exact center of the mural, she paints a circular design with a diameter of 30 cm. If a drop of paint splatters and lands at a completely random point on the mural, what is the probability that it lands inside the circular design? Express your answer as a simplified fraction using π.
    Answer: ______________
  6. Matiu is designing a large rectangular banner for a school event. The banner measures 120 cm in length and 80 cm in width. In the center of the banner, he paints a circular logo with a diameter of 40 cm. If a bird drops a feather that lands at a completely random point on the banner, what is the probability that the feather lands on the circular logo? Express your answer as a simplified fraction using π. Answer: ______________
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Answer Key & Explanations

Probability Concepts · Grade 7 · Worksheet 2

  1. P(drawing a card numbered with a multiple of 11 from a bag containing cards numbered 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220) = ? Answer: 1 Solution: Count the total number of cards in the bag. The cards are numbered 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220. That is 20 cards total.
    Full step-by-step solution

    Step 1: Count the total number of cards in the bag. The cards are numbered 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220. That is 20 cards total. Step 2: Identify the favorable outcomes. The problem asks for drawing a card with a multiple of 11. All numbers listed are multiples of 11, so all 20 cards are favorable. Step 3: Calculate the probability. Probability = (Number of favorable outcomes) / (Total number of outcomes) = 20/20. Step 4: Simplify the fraction. 20/20 = 1. The answer is 1.

  2. P(rolling a 1, 3, or 5 on a fair six-sided die) = ? Answer: 1/2 Solution: Identify the total number of outcomes on a fair six-sided die. There are 6 possible outcomes (1, 2, 3, 4, 5, 6). Identify the favorable outcomes.
    Full step-by-step solution

    Step 1: Identify the total number of outcomes on a fair six-sided die. There are 6 possible outcomes (1, 2, 3, 4, 5, 6). Step 2: Identify the favorable outcomes. The problem asks for rolling a 1, 3, or 5. These are 3 outcomes. Step 3: Calculate the probability. Probability = (Number of favorable outcomes) / (Total number of outcomes) = 3/6. Step 4: Simplify the fraction. 3/6 simplifies to 1/2. The answer is 1/2.

  3. P(drawing a card numbered with an odd number from a bag containing cards numbered 1, 3, 5, 7, 9, 11, 13, 15, 17, 19) = ? Answer: 1 Solution: Count the total number of cards in the bag. The cards are numbered 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. That is 10 cards.
    Full step-by-step solution

    Step 1: Count the total number of cards in the bag. The cards are numbered 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. That is 10 cards. Step 2: Identify the favorable outcomes. The problem asks for drawing a card with an odd number. All numbers listed are odd, so all 10 cards are favorable. Step 3: Calculate the probability. Probability = (Number of favorable outcomes) / (Total number of outcomes) = 10/10. Step 4: Simplify the fraction. 10/10 = 1. The answer is 1.

  4. P(rolling a 3 on a fair six-sided die) = ? Answer: 1/6 Solution: We are asked for the probability of rolling a 3 on a fair six-sided die. Identify the total number of possible outcomes. A fair six-sided die has 6 faces, numbered 1, 2, 3, 4, 5, and 6.
    Full step-by-step solution

    Step 1: Understand the problem. We are asked for the probability of rolling a 3 on a fair six-sided die. Step 2: Identify the total number of possible outcomes. A fair six-sided die has 6 faces, numbered 1, 2, 3, 4, 5, and 6. Therefore, the total number of possible outcomes when you roll the die is 6. Step 3: Identify the number of favorable outcomes. A "favorable outcome" is the one we are looking for, which is rolling a 3. Only one face of the die shows the number 3. Therefore, the number of favorable outcomes is 1. Step 4: Apply the probability formula. The probability of an event is given by: Probability = (Number of favorable outcomes) / (Total number of possible outcomes) Step 5: Substitute the numbers into the formula. Number of favorable outcomes = 1 Total number of possible outcomes = 6 So, Probability = 1 / 6 Step 6: State the final answer. The probability of rolling a 3 is 1/6.

  5. Hana is creating a large square mural for a community art project. The square mural has a side length of 120 cm. In the exact center of the mural, she paints a circular design with a diameter of 30 cm. If a drop of paint splatters and lands at a completely random point on the mural, what is the probability that it lands inside the circular design? Express your answer as a simplified fraction using π. Answer: π/64 Solution: Find the area of the square mural. Area of square = side × side = 120 cm × 120 cm = 14400 square cm. Find the radius of the circular design.
    Full step-by-step solution

    Step 1: Find the area of the square mural. Area of square = side × side = 120 cm × 120 cm = 14400 square cm. Step 2: Find the radius of the circular design. The diameter is 30 cm, so the radius is half of that: radius = 30 ÷ 2 = 15 cm. Step 3: Find the area of the circular design. Area of circle = π × radius² = π × (15 cm)² = π × 225 = 225π square cm. Step 4: Write the probability as a fraction. Probability = (area of circle) / (area of square) = (225π) / 14400. Step 5: Simplify the fraction. Both 225 and 14400 are divisible by 225. 225 ÷ 225 = 1, and 14400 ÷ 225 = 64. So the fraction simplifies to π/64. Since π is an irrational number and 1 and 64 have no common factors, the fraction π/64 is in simplest form. The answer is π/64.

  6. Matiu is designing a large rectangular banner for a school event. The banner measures 120 cm in length and 80 cm in width. In the center of the banner, he paints a circular logo with a diameter of 40 cm. If a bird drops a feather that lands at a completely random point on the banner, what is the probability that the feather lands on the circular logo? Express your answer as a simplified fraction using π. Answer: π/96 Solution: Find the area of the rectangular banner. Area = length × width = 120 cm × 80 cm = 9600 square cm. Find the radius of the circular logo.
    Full step-by-step solution

    Step 1: Find the area of the rectangular banner. Area = length × width = 120 cm × 80 cm = 9600 square cm. Step 2: Find the radius of the circular logo. Diameter = 40 cm, so radius = 40 ÷ 2 = 20 cm. Step 3: Find the area of the circular logo. Area = π × radius² = π × (20 cm)² = 400π square cm. Step 4: Calculate the probability. Probability = (area of circle) / (area of rectangle) = (400π) / 9600. Step 5: Simplify the fraction. Divide numerator and denominator by 400: (400π ÷ 400) / (9600 ÷ 400) = π/24. Further simplify by dividing numerator and denominator by 4: π/96. The fraction π/96 is already in simplest form. The answer is π/96.