CBSE MATHEMATICS • SELECTED CENTRAL & STATE COMPETITIVE EXAMS
AIMSSchool of MathematicsAim through AIMS
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GANITA MANJARI · GRADE 9 · PART I · CHAPTER 7

Practice

Think first. Use AI purposefully. Verify always.

Seven AIMS sprints. State your model before calculating. Use exact fractions when decimals recur. Feedback supports practice; these are not timed examination results.

Sprint 1 — CHANCE & SCALE

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Q1. Which claim about two possible outcomes is justified?
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Q2. If P(E) = 0.3, find P(not E).
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Q3. A match may end in win, draw or loss. If P(win) = 0.5, which conclusion follows?
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Sprint 2 — EXPERIMENTAL

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Q1. In 50 rolls, a die shows 4 eight times. Enter the observed relative frequency of 4.
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Q2. A 3 occurs three times in twelve rolls. Enter its experimental probability.
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Q3. No toss has been made yet. What is the observed relative frequency of heads?
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Sprint 3 — THEORETICAL

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Q1. A fair six-sided die is rolled. Enter P(result greater than 4) as a fraction.
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Q2. Eleven equally selectable letter cards spell PROBABILITY. Enter P(B).
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Q3. A bag has 3 red and 7 blue equally selectable balls. Enter P(red).
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Sprint 4 — SAMPLE SPACE & EVENTS

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Q1. Two independent fair tosses: enter P(at least one head).
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Q2. Three independent fair tosses: are head counts 0,1,2,3 equally likely?
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Q3. Record a coin result and a card numbered 1–6. Enter n(S).
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Sprint 5 — TREE DIAGRAMS

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Q1. From 4 red and 5 blue balls, a red is removed. Enter P(blue on the second draw).
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Q2. From the same bag, draw twice without replacement. Enter P(red then blue).
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Q3. Two independent fair coin tosses: enter P(one head and one tail).
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Sprint 6 — DATA & SAMPLING

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Q1. A representative sample of 30 sweets includes 7 yellow. Estimate the yellow count in 600 sweets.
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Q2. A sample of 40 students includes 9 who prefer Sports Club. Estimate the count in a school of 800.
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Q3. Which change addresses coverage bias in a school survey?
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Sprint 7 — MIXED MASTERY

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Q1. After six independent fair tosses all show H, enter P(T on the next toss).
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Q2. Draw twice from four distinct numbered balls without replacement. Enter the number of ordered outcomes.
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Q3. What justifies using a circle-to-rectangle area ratio as a landing probability?
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Q4. A longer fair-coin simulation must always move closer to 1/2. Is that statement justified?
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