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Math Chapter 11 : Topic 5
Relative Frequency
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A coin is tossed $50$ times and heads appear $28$ times. The relative frequency of heads is:
Reasoning: Relative frequency $=$ Number of favorable outcomes $/$ Total trials$= 28\ /\ 50 = 0.56$
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Which statement best describes relative frequency?
Reasoning: Relative frequency is based on experimental results, not theoretical outcomes.
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A die is rolled $120$ times and the number $4$ appears $18$ times. What is the experimental probability of getting $4$?
Reasoning: $18\ /\ 120 = 0.15$
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As the number of trials increases, the relative frequency tends to:
Reasoning: This follows the Law of Large Numbers.
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In an experiment, the relative frequency of an event is $0.8$ after many trials. This suggests:
Reasoning: A value close to $1$ indicates high likelihood.
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If an event never occurs in $100$ trials, its relative frequency is:
Reasoning: $0$ occurrences $/\ 100$ trials $= 0$
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A spinner is spun $200$ times and lands on red $50$ times. What is the relative frequency of red?
Reasoning: $50/200 = 0.25$
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Which of the following is an example of experimental probability?
Reasoning: Experimental probability $=$ relative frequency from actual trials.
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A student records rainfall on $12$ days and finds rain on $3$ days. The relative frequency of rain is:
Reasoning: $3/12 = 0.25$
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Which factor improves the accuracy of relative frequency as an estimate?
Reasoning: More trials give a better estimate of true probability.
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A coin is tossed repeatedly. After many trials, the relative frequency of heads is $0.49$. This indicates:
Reasoning: Close to $0.5$ suggests fairness.
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If relative frequency $= 1$, then the event is:
Reasoning: Occurred in all trials$\ \ \ \ \Longrightarrow \ \ \ \ $certain event.
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A bag is tested experimentally and red ball appears $45$ times in $90$ draws. Estimated probability of red ball is:
Reasoning: $45/90 = 0.5$
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Which of the following best explains why relative frequency may differ from theoretical probability?
Reasoning: Small sample size causes variation.
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If relative frequency of success increases with trials, it means:
Reasoning: More trials stabilize results.
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A coin is tossed $10$ times and heads appears $7$ times. The relative frequency is:
Reasoning: Small sample$\ \ \ \ \Longrightarrow \ \ \ \ $less reliable.
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Which situation best demonstrates relative frequency?
Reasoning: Relative frequency depends on observations.
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In $500$ trials, event $A$ occurs $125$ times. Relative frequency of $A$ is:
Reasoning: $125\ /\ 500 = 0.25$
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If an event has relative frequency close to $0$, it is:
Reasoning: Very low occurrence indicates rarity.
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Which of the following values is NOT possible for relative frequency?
Reasoning: Relative frequency lies between $0$ and $1$.
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Relative frequency is mainly used to:
Reasoning: Used when theoretical probability is unknown.
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A spinner experiment gives relative frequency $0.33$ for blue. This implies:
Reasoning: It is an estimate, not exact value.
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When trials increase from $100$ to $1000$, relative frequency:
Reasoning: Larger sample improves reliability.
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Relative frequency depends on:
Reasoning: It is calculated from observed results.
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If event occurs $60$ times in $200$ trials, its relative frequency is:
Reasoning: $60\ /\ 200 = 0.30$
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