FBISE, NCP & NBF-aligned resources for Classes 9–12
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Math Chapter 11 : Topic 7
Frequency Applications
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A factory machine produces defective bulbs. Out of $200$ tested bulbs, $20$ are defective. If $500$ bulbs are produced, the expected number of defective bulbs is:
Reasoning: Relative frequency $= 20\ /\ 200 = 0.1$Expected $= 0.1 \times 500 = 50$
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In a survey, $15$ out of $60$ people prefer tea. Estimate how many out of $300$ people will prefer tea.
Reasoning: Relative frequency $= 15/60 = 1/4\ \ \ \ \Longrightarrow \ \ \ \ 300 \times 1/4 = 75$
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A basketball player scores in $18$ out of $30$ attempts. Predict scores in $100$ attempts.
Reasoning: $18/30 = 0.6\ \ \ \ \Longrightarrow \ \ \ \ 100 \times 0.6 = 60$
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A weather report shows rain on $12$ out of $40$ days. Expected rainy days in $200$ days:
Reasoning: $12/40 = 0.3\ \ \ \ \Longrightarrow \ \ \ \ 200 \times 0.3 = 60$
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A die is rolled $90$ times and '$6$' appears $10$ times. Estimate its occurrence in $450$ rolls.
Reasoning: $10/90 = 1/9\ \ \ \ \Longrightarrow \ \ \ \ 450 \times 1/9 = 50$
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A shopkeeper observes that $8$ out of $50$ customers buy a product. Estimate buyers in $500$ customers.
Reasoning: $8/50 = 0.16\ \ \ \ \Longrightarrow \ \ \ \ 500 \times 0.16 = 80$
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A cricket player hits a boundary in $25$ out of $100$ balls. Expected boundaries in $400$ balls:
Reasoning: $25/100 = 0.25\ \ \ \ \Longrightarrow \ \ \ \ 400 \times 0.25 = 100$
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Out of $120$ students, $30$ failed a test. Estimate failures in a group of $600$ students.
Reasoning: $30/120 = 1/4\ \ \ \ \Longrightarrow \ \ \ \ 600 \times 1/4 = 150$
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A bag contains unknown colored balls. In $40$ draws, red appears $10$ times. Expected reds in $200$ draws:
Reasoning: $10/40 = 0.25\ \ \ \ \Longrightarrow \ \ \ \ 200 \times 0.25 = 50$
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A student answers $36$ out of $60$ questions correctly. Estimate correct answers out of $150$ questions.
Reasoning: $36/60 = 0.6\ \ \ \ \Longrightarrow \ \ \ \ 150 \times 0.6 = 90$
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A car passes inspection in $48$ out of $60$ cases. Expected passes in $300$ cases:
Reasoning: $48/60 = 0.8\ \ \ \ \Longrightarrow \ \ \ \ 300 \times 0.8 = 240$
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A coin shows heads $45$ times in $90$ tosses. Expected heads in $180$ tosses:
Reasoning: $45/90 = 0.5\ \ \ \ \Longrightarrow \ \ \ \ 180 \times 0.5 = 90$
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In a hospital, $6$ out of $30$ patients recover quickly. Estimate quick recoveries among $150$ patients.
Reasoning: $6/30 = 0.2\ \ \ \ \Longrightarrow \ \ \ \ 150 \times 0.2 = 30$
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A factory observes $3$ defective items in $25$. Estimate defective items in $100$ items.
Reasoning: $3/25 = 0.12\ \ \ \ \Longrightarrow \ \ \ \ 100 \times 0.12 = 12$
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If relative frequency of success is $0.75$, expected successes in $80$ trials:
Reasoning: $0.75 \times 80 = 60$
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A survey shows $18\%$ people prefer online shopping. Estimate number out of $500$:
Reasoning: $0.18 \times 500 = 90$
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A machine works correctly $92$ out of $100$ times. Expected correct operations in $1000$ runs:
Reasoning: $0.92 \times 1000 = 920$
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A student guesses answers correctly $1$ out of $5$ times. Expected correct answers in $50$ questions:
Reasoning: $1/5 = 0.2\ \ \ \ \Longrightarrow \ \ \ \ 50 \times 0.2 = 10$
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A spinner lands on blue $14$ times in $70$ spins. Expected in $350$ spins:
Reasoning: $14/70 = 0.2\ \ \ \ \Longrightarrow \ \ \ \ 350 \times 0.2 = 70$
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A football team wins $9$ out of $15$ matches. Expected wins in $45$ matches:
Reasoning: $9/15 = 0.6\ \ \ \ \Longrightarrow \ \ \ \ 45 \times 0.6 = 27$
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A product has a $5\%$ defect rate. Expected defects in $200$ items:
Reasoning: $0.05 \times 200 = 10$
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In $80$ trials, an event occurs $32$ times. Predict occurrences in $200$ trials:
Reasoning: $32/80 = 0.4\ \ \ \ \Longrightarrow \ \ \ \ 200 \times 0.4 = 80$
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A driver has accidents in $2$ out of $50$ trips. Expected accidents in $500$ trips:
Reasoning: $2/50 = 0.04\ \ \ \ \Longrightarrow \ \ \ \ 500 \times 0.04 = 20$
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A class survey shows $40\%$ students like math. Expected number in $250$ students:
Reasoning: $0.4 \times 250 = 100$
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A coin shows tails $18$ times in $30$ tosses. Expected tails in $90$ tosses:
Reasoning: $18/30 = 0.6\ \ \ \ \Longrightarrow \ \ \ \ 90 \times 0.6 = 54$
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