Design Simulations for Compound Events - 7th Grade Math
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What is the definition of experimental probability from a simulation?
What is the definition of experimental probability from a simulation?
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$\frac{\text{number of successes}}{\text{number of trials}}$. Ratio of favorable outcomes to total attempts.
$\frac{\text{number of successes}}{\text{number of trials}}$. Ratio of favorable outcomes to total attempts.
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If $P(\text{type A})=0.40$, what is the expected number of donors needed to find $1$ type A donor?
If $P(\text{type A})=0.40$, what is the expected number of donors needed to find $1$ type A donor?
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$\frac{1}{0.40}=2.5$. Average trials needed = $\frac{1}{\text{probability}}$.
$\frac{1}{0.40}=2.5$. Average trials needed = $\frac{1}{\text{probability}}$.
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What is one correct way to simulate a probability of $0.30$ using random digits $0$–$9$?
What is one correct way to simulate a probability of $0.30$ using random digits $0$–$9$?
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Let $0,1,2$ represent success; $3$–$9$ represent failure. $3$ of $10$ digits gives $\frac{3}{10}=0.30$ probability.
Let $0,1,2$ represent success; $3$–$9$ represent failure. $3$ of $10$ digits gives $\frac{3}{10}=0.30$ probability.
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What is the expected number of trials to get $1$ success if $P(\text{success})=p$?
What is the expected number of trials to get $1$ success if $P(\text{success})=p$?
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$\frac{1}{p}$. Reciprocal of probability gives expected trials.
$\frac{1}{p}$. Reciprocal of probability gives expected trials.
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In $200$ trials, “A then B” occurred $46$ times. What is the relative frequency?
In $200$ trials, “A then B” occurred $46$ times. What is the relative frequency?
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$\frac{46}{200}=0.23$. Frequency divided by total trials gives relative frequency.
$\frac{46}{200}=0.23$. Frequency divided by total trials gives relative frequency.
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Identify the probability model for simulating “donor has type A blood” if $P(A)=0.40$.
Identify the probability model for simulating “donor has type A blood” if $P(A)=0.40$.
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Use $10$ digits; let $0$–$3$ mean type A and $4$–$9$ mean not A. $4$ of $10$ digits represents $0.40$ probability.
Use $10$ digits; let $0$–$3$ mean type A and $4$–$9$ mean not A. $4$ of $10$ digits represents $0.40$ probability.
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What is the experimental probability if $18$ successes occur in $60$ simulation trials?
What is the experimental probability if $18$ successes occur in $60$ simulation trials?
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$\frac{18}{60}=0.30$. Divide successes by total trials for experimental probability.
$\frac{18}{60}=0.30$. Divide successes by total trials for experimental probability.
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What is one correct way to simulate a probability of $\frac{3}{8}$ using equally likely outcomes?
What is one correct way to simulate a probability of $\frac{3}{8}$ using equally likely outcomes?
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Use $8$ equally likely outcomes; mark $3$ as “success”. $\frac{3}{8}$ requires $3$ successes out of $8$ total outcomes.
Use $8$ equally likely outcomes; mark $3$ as “success”. $\frac{3}{8}$ requires $3$ successes out of $8$ total outcomes.
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Which tool best simulates outcomes with probabilities $\frac{1}{4}$, $\frac{1}{2}$, $\frac{1}{4}$?
Which tool best simulates outcomes with probabilities $\frac{1}{4}$, $\frac{1}{2}$, $\frac{1}{4}$?
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A spinner divided into $4$ equal sections labeled to match the ratios. Sections match the given probability ratios exactly.
A spinner divided into $4$ equal sections labeled to match the ratios. Sections match the given probability ratios exactly.
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What is a simulation in probability for a compound event?
What is a simulation in probability for a compound event?
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A model using random trials to estimate a compound event’s probability. Uses randomness to mimic real-world compound events repeatedly.
A model using random trials to estimate a compound event’s probability. Uses randomness to mimic real-world compound events repeatedly.
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What is the relative frequency of an event in a simulation?
What is the relative frequency of an event in a simulation?
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$\frac{\text{number of successes}}{\text{total trials}}$. Counts successes divided by total attempts in the experiment.
$\frac{\text{number of successes}}{\text{total trials}}$. Counts successes divided by total attempts in the experiment.
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What is the addition rule for mutually exclusive events $A$ and $B$?
What is the addition rule for mutually exclusive events $A$ and $B$?
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$P(A \text{ or } B)=P(A)+P(B)$. Add probabilities when events can't happen simultaneously.
$P(A \text{ or } B)=P(A)+P(B)$. Add probabilities when events can't happen simultaneously.
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Which option best represents a fair simulation for $P(A)=0.3$ using digits?
Which option best represents a fair simulation for $P(A)=0.3$ using digits?
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Use digits $0$–$9$; let $0,1,2$ represent event $A$. $3$ of $10$ digits gives $30%$ chance, matching the probability.
Use digits $0$–$9$; let $0,1,2$ represent event $A$. $3$ of $10$ digits gives $30%$ chance, matching the probability.
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Which option best represents a fair simulation for $P(A)=\frac{1}{4}$ using cards?
Which option best represents a fair simulation for $P(A)=\frac{1}{4}$ using cards?
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Use $4$ equally likely cards; label $1$ card as success. $1$ out of $4$ cards gives $25%$ chance, matching the probability.
Use $4$ equally likely cards; label $1$ card as success. $1$ out of $4$ cards gives $25%$ chance, matching the probability.
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What is the estimated probability of success if $12$ of $50$ simulated donors have type A?
What is the estimated probability of success if $12$ of $50$ simulated donors have type A?
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$\frac{12}{50}=0.24$. Divide type A donors by total donors tested.
$\frac{12}{50}=0.24$. Divide type A donors by total donors tested.
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If $P(A)=0.4$ and $P(B)=0.5$ are independent, what is $P(A \text{ and } B)$?
If $P(A)=0.4$ and $P(B)=0.5$ are independent, what is $P(A \text{ and } B)$?
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$0.4\cdot 0.5=0.2$. Multiply probabilities for independent events occurring together.
$0.4\cdot 0.5=0.2$. Multiply probabilities for independent events occurring together.
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What is the estimated probability if a simulation has $18$ successes in $60$ trials?
What is the estimated probability if a simulation has $18$ successes in $60$ trials?
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$\frac{18}{60}=0.3$. Divide successes by total trials to get experimental probability.
$\frac{18}{60}=0.3$. Divide successes by total trials to get experimental probability.
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What is the experimental probability (estimate) after a simulation?
What is the experimental probability (estimate) after a simulation?
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The event’s relative frequency from the trials. The simulation's success rate approximates the true probability.
The event’s relative frequency from the trials. The simulation's success rate approximates the true probability.
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What does it mean for two events to be independent in a simulation?
What does it mean for two events to be independent in a simulation?
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One event’s outcome does not change the other’s probability. Like flipping two coins - first flip doesn't affect second.
One event’s outcome does not change the other’s probability. Like flipping two coins - first flip doesn't affect second.
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Identify the correct simulation tool for $P(A)=\frac{2}{5}$ using a spinner.
Identify the correct simulation tool for $P(A)=\frac{2}{5}$ using a spinner.
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A spinner with $5$ equal sections, with $2$ labeled success. $2$ out of $5$ sections gives $40%$ chance, matching the probability.
A spinner with $5$ equal sections, with $2$ labeled success. $2$ out of $5$ sections gives $40%$ chance, matching the probability.
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Which choice gives the best estimate in a simulation: $20$ trials or $200$ trials?
Which choice gives the best estimate in a simulation: $20$ trials or $200$ trials?
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$200$ trials. More trials reduce sampling error and improve accuracy.
$200$ trials. More trials reduce sampling error and improve accuracy.
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What is the expected number of trials to get one success if $P(\text{success})=\frac{1}{8}$?
What is the expected number of trials to get one success if $P(\text{success})=\frac{1}{8}$?
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$\frac{1}{\frac{1}{8}}=8$. Reciprocal of probability gives expected trials to first success.
$\frac{1}{\frac{1}{8}}=8$. Reciprocal of probability gives expected trials to first success.
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What is the expected number of trials to get one success if $P(\text{success})=0.2$?
What is the expected number of trials to get one success if $P(\text{success})=0.2$?
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$\frac{1}{0.2}=5$. Expected trials equals $1$ divided by success probability.
$\frac{1}{0.2}=5$. Expected trials equals $1$ divided by success probability.
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In a simulation, what is one trial when modeling “donor is type A and Rh$+$”?
In a simulation, what is one trial when modeling “donor is type A and Rh$+$”?
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One randomly generated donor outcome for both blood type and Rh factor. Each trial tests both characteristics of one donor.
One randomly generated donor outcome for both blood type and Rh factor. Each trial tests both characteristics of one donor.
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What is the probability a simulated donor is not type A if $P(\text{A})=0.24$?
What is the probability a simulated donor is not type A if $P(\text{A})=0.24$?
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$1-0.24=0.76$. Complement rule: subtract from $1$ for "not" events.
$1-0.24=0.76$. Complement rule: subtract from $1$ for "not" events.
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