Approximate Probability From Collected Data - 7th Grade Math
Card 1 of 25
What is the experimental probability of an event in $n$ trials with $k$ successes?
What is the experimental probability of an event in $n$ trials with $k$ successes?
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$\frac{k}{n}$. Divide successes by total trials to get experimental probability.
$\frac{k}{n}$. Divide successes by total trials to get experimental probability.
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What is the theoretical probability of rolling a $3$ or $6$ on a fair number cube?
What is the theoretical probability of rolling a $3$ or $6$ on a fair number cube?
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$\frac{2}{6}=\frac{1}{3}$. Two favorable outcomes (3 or 6) out of six equally likely outcomes.
$\frac{2}{6}=\frac{1}{3}$. Two favorable outcomes (3 or 6) out of six equally likely outcomes.
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Identify whether this is reasonable: with $p=\frac{1}{2}$ and $n=100$, predict exactly $50$ successes.
Identify whether this is reasonable: with $p=\frac{1}{2}$ and $n=100$, predict exactly $50$ successes.
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Not guaranteed; $50$ is an estimate, not exact. Predictions give expected values, not exact guarantees.
Not guaranteed; $50$ is an estimate, not exact. Predictions give expected values, not exact guarantees.
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If the experimental probability is $\frac{9}{50}$, what is the predicted count in $500$ trials?
If the experimental probability is $\frac{9}{50}$, what is the predicted count in $500$ trials?
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$500\cdot\frac{9}{50}=90$. Scale up: multiply trials by experimental probability.
$500\cdot\frac{9}{50}=90$. Scale up: multiply trials by experimental probability.
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Which value is the best estimate of probability from $7$ successes in $20$ trials?
Which value is the best estimate of probability from $7$ successes in $20$ trials?
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$\frac{7}{20}=0.35$. Best estimate uses the experimental probability formula $\frac{k}{n}$.
$\frac{7}{20}=0.35$. Best estimate uses the experimental probability formula $\frac{k}{n}$.
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Find and correct the estimate: $p=\frac{1}{4}$ and $n=200$ gives $200\cdot\frac{1}{4}=40$.
Find and correct the estimate: $p=\frac{1}{4}$ and $n=200$ gives $200\cdot\frac{1}{4}=40$.
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Correct: $200\cdot\frac{1}{4}=50$. Error found: $200 \times \frac{1}{4} = 50$, not 40.
Correct: $200\cdot\frac{1}{4}=50$. Error found: $200 \times \frac{1}{4} = 50$, not 40.
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A bag has $5$ blue and $15$ total; predict blue draws in $90$ draws with replacement.
A bag has $5$ blue and $15$ total; predict blue draws in $90$ draws with replacement.
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$90\cdot\frac{5}{15}=30$. Expected blues: $90 \times \frac{5}{15} = 90 \times \frac{1}{3} = 30$.
$90\cdot\frac{5}{15}=30$. Expected blues: $90 \times \frac{5}{15} = 90 \times \frac{1}{3} = 30$.
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A spinner has $8$ equal sections; predict hits on red in $160$ spins if $p=\frac{3}{8}$.
A spinner has $8$ equal sections; predict hits on red in $160$ spins if $p=\frac{3}{8}$.
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$160\cdot\frac{3}{8}=60$. Expected hits: multiply spins by probability of red section.
$160\cdot\frac{3}{8}=60$. Expected hits: multiply spins by probability of red section.
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Predict the approximate relative frequency of an event with $p=0.12$ over many trials.
Predict the approximate relative frequency of an event with $p=0.12$ over many trials.
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$0.12$. Relative frequency approaches the given probability value.
$0.12$. Relative frequency approaches the given probability value.
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Predict how many times a $3$ or $6$ appears in $600$ fair die rolls using $p=\frac{1}{3}$.
Predict how many times a $3$ or $6$ appears in $600$ fair die rolls using $p=\frac{1}{3}$.
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$600\cdot\frac{1}{3}=200$. Expected value: multiply trials by combined probability $\frac{2}{6}=\frac{1}{3}$.
$600\cdot\frac{1}{3}=200$. Expected value: multiply trials by combined probability $\frac{2}{6}=\frac{1}{3}$.
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Predict how many times a $6$ appears in $300$ fair die rolls using $p=\frac{1}{6}$.
Predict how many times a $6$ appears in $300$ fair die rolls using $p=\frac{1}{6}$.
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$300\cdot\frac{1}{6}=50$. Expected value: multiply trials by probability of rolling 6.
$300\cdot\frac{1}{6}=50$. Expected value: multiply trials by probability of rolling 6.
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Predict the number of heads in $80$ fair coin tosses using $p=\frac{1}{2}$.
Predict the number of heads in $80$ fair coin tosses using $p=\frac{1}{2}$.
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$80\cdot\frac{1}{2}=40$. Expected value: multiply trials by probability of heads.
$80\cdot\frac{1}{2}=40$. Expected value: multiply trials by probability of heads.
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Find the relative frequency if an event occurs $45$ times in $200$ trials.
Find the relative frequency if an event occurs $45$ times in $200$ trials.
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$\frac{45}{200}=0.225$. Divide occurrences by trials to get relative frequency as decimal.
$\frac{45}{200}=0.225$. Divide occurrences by trials to get relative frequency as decimal.
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Find the experimental probability if an event happens $18$ times in $60$ trials.
Find the experimental probability if an event happens $18$ times in $60$ trials.
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$\frac{18}{60}=\frac{3}{10}$. Divide occurrences by trials: $\frac{18}{60}$ simplifies to $\frac{3}{10}$.
$\frac{18}{60}=\frac{3}{10}$. Divide occurrences by trials: $\frac{18}{60}$ simplifies to $\frac{3}{10}$.
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What is the relative frequency of an event after $n$ trials with $k$ occurrences?
What is the relative frequency of an event after $n$ trials with $k$ occurrences?
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$\frac{k}{n}$. Relative frequency equals occurrences divided by total trials.
$\frac{k}{n}$. Relative frequency equals occurrences divided by total trials.
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What does long-run relative frequency approach as the number of trials becomes large?
What does long-run relative frequency approach as the number of trials becomes large?
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It approaches the theoretical probability. Law of large numbers: experimental converges to theoretical probability.
It approaches the theoretical probability. Law of large numbers: experimental converges to theoretical probability.
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What is the predicted number of successes in $n$ trials for probability $p$?
What is the predicted number of successes in $n$ trials for probability $p$?
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$n\cdot p$. Multiply trials by probability to predict expected successes.
$n\cdot p$. Multiply trials by probability to predict expected successes.
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What is the predicted relative frequency for an event with probability $p$?
What is the predicted relative frequency for an event with probability $p$?
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$p$. Relative frequency equals the theoretical probability in the long run.
$p$. Relative frequency equals the theoretical probability in the long run.
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Identify the formula to estimate probability from data: occurrences $k$, trials $n$.
Identify the formula to estimate probability from data: occurrences $k$, trials $n$.
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$\hat{p}=\frac{k}{n}$. Sample proportion formula: successes over trials estimates probability.
$\hat{p}=\frac{k}{n}$. Sample proportion formula: successes over trials estimates probability.
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What is the theoretical probability of rolling a $3$ on a fair number cube?
What is the theoretical probability of rolling a $3$ on a fair number cube?
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$\frac{1}{6}$. One favorable outcome (3) out of six equally likely outcomes.
$\frac{1}{6}$. One favorable outcome (3) out of six equally likely outcomes.
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Identify the probability of rolling a $3$ or $6$ on a fair number cube.
Identify the probability of rolling a $3$ or $6$ on a fair number cube.
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$\frac{2}{6}=\frac{1}{3}$. Two favorable outcomes ($3$ or $6$) out of six total.
$\frac{2}{6}=\frac{1}{3}$. Two favorable outcomes ($3$ or $6$) out of six total.
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What happens to the typical variability of relative frequency as the number of trials increases?
What happens to the typical variability of relative frequency as the number of trials increases?
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It decreases (results become more stable). More trials reduce random fluctuations in frequency.
It decreases (results become more stable). More trials reduce random fluctuations in frequency.
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If $p(A)=0.3$ and there are $200$ trials, what is the predicted count of $A$?
If $p(A)=0.3$ and there are $200$ trials, what is the predicted count of $A$?
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$200\times^0.3=60$. Multiply trials by probability: $200 \times 0.3$.
$200\times^0.3=60$. Multiply trials by probability: $200 \times 0.3$.
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If an event happens $45$ times in $100$ trials, what is the experimental probability?
If an event happens $45$ times in $100$ trials, what is the experimental probability?
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$\frac{45}{100}=0.45$. Experimental probability equals relative frequency.
$\frac{45}{100}=0.45$. Experimental probability equals relative frequency.
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If an event has probability $p=0.75$, what approximate relative frequency should you predict?
If an event has probability $p=0.75$, what approximate relative frequency should you predict?
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$\approx^0.75$. Relative frequency approaches the given probability.
$\approx^0.75$. Relative frequency approaches the given probability.
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