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Math Chapter 11 : Topic 6
Frequency Applications
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A die is rolled $60$ times. What is the expected frequency of getting a $3$?
Reasoning: Probability of $3 = 1/6$Expected frequency $= 60 \times (1/6) = 10$
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Expected frequency is calculated by:
Reasoning: Expected frequency $=$ Probability $\times$ Number of trials
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A coin is tossed $200$ times. Expected number of heads is:
Reasoning: Probability of head $= 1/2\ \ \ \ \Longrightarrow \ \ \ \ 200 \times 1/2 = 100$
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If probability of an event is $0.25$ and total trials are $80$, expected frequency is:
Reasoning: $0.25 \times 80 = 20$
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A spinner has $5$ equal sections. It is spun $150$ times. Expected frequency of landing on one section:
Reasoning: Probability $= 1/5\ \ \ \ \Longrightarrow \ \ \ \ 150 \times 1/5 = 30$
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If an event is impossible, its expected frequency is:
Reasoning: Probability $= 0\ \ \ \ \Longrightarrow \ \ \ \ $Expected frequency $= 0$
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Expected frequency of an event depends on:
Reasoning: It uses both probability and total trials.
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A bag contains $4$ red and $6$ blue balls. One ball is drawn $100$ times with replacement. Expected frequency of red:
Reasoning: Probability of red $= 4/10 = 0.4\ \ \ \ \Longrightarrow \ \ \ \ 100 \times 0.4 = 40$
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If expected frequency is $25$ and probability is $0.5$, number of trials is:
Reasoning: Trials $= 25 \div 0.5 = 50$
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Expected frequency is best described as:
Reasoning: It is a theoretical prediction.
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A die is rolled $120$ times. Expected frequency of getting an even number:
Reasoning: Even numbers $= 3/6 = 1/2\ \ \ \ \Longrightarrow \ \ \ \ 120 \times 1/2 = 60$
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If probability of rain is $0.3$ for a day, expected rainy days in $50$ days:
Reasoning: $0.3 \times 50 = 15$
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A card is drawn $52$ times (with replacement). Expected frequency of getting a king:
Reasoning: Kings $= 4/52 = 1/13\ \ \ \ \Longrightarrow \ \ \ \ 52 \times 1/13 = 4$
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If expected frequency is greater than observed frequency, it suggests:
Reasoning: Observed value is lower than predicted.
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Expected frequency becomes more reliable when:
Reasoning: More trials improve prediction accuracy.
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A fair coin is tossed $10$ times. Expected frequency of tails is:
Reasoning: $10 \times 1/2 = 5$
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A die is rolled $n$ times. Expected frequency of getting $6$ is $15$. Value of $n$ is:
Reasoning: $n \times (1/6) = 15\ \ \ \ \Longrightarrow \ \ \ \ n = 90$
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Which of the following is true?
Reasoning: It is theoretical, not exact.
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Probability $= 0.8$ and trials $= 50$. Expected frequency:
Reasoning: $0.8 \times 50 = 40$
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Expected frequency cannot be:
Reasoning: Frequency cannot be negative.
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A bag has $2$ green, $3$ red balls. In $100$ trials, expected frequency of green:
Reasoning: Probability $= 2/5\ \ \ \ \Longrightarrow \ \ \ \ 100 \times 2/5 = 40$
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If expected frequency is $0$, probability must be:
Reasoning: Only probability $0$ gives expected frequency $0$.
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Expected frequency of a certain event in $70$ trials is:
Reasoning: Probability $= 1\ \ \ \ \Longrightarrow \ \ \ \ $ Expected frequency $= 70$
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A spinner has unequal sections. Expected frequency depends on:
Reasoning: Unequal probabilities must be considered.
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Expected frequency is mainly used to:
Reasoning: It predicts expected occurrences.
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