Design Simulations for Compound Events - 7th Grade Math

1. What is a simulation in probability for a compound event?

   A model using random trials to estimate a compound event's probability. Uses randomness to mimic real-world compound events repeatedly.

2. Which tool best simulates outcomes with probabilities $\frac{1}{4}$, $\frac{1}{2}$, $\frac{1}{4}$?

   A spinner divided into $4$ equal sections labeled to match the ratios. Sections match the given probability ratios exactly.

3. Which choice gives the best estimate in a simulation: $20$ trials or $200$ trials?

   $200$ trials. More trials reduce sampling error and improve accuracy.

4. A simulation uses digits $0$–$9$ for $P(\text{success})=0.30$. Which digits should represent success?

   Any $3$ digits, such as $0,1,2$. $3$ digits out of $10$ gives $0.30$ probability.

5. What is one correct way to simulate a probability of $0.30$ using random digits $0$–$9$?

   Let $0,1,2$ represent success; $3$–$9$ represent failure. $3$ of $10$ digits gives $\frac{3}{10}=0.30$ probability.

6. If $P(A)=0.20$ and $P(B)=0.50$ are independent, what is $P(A\text{ and }B)$?

   $0.20\times 0.50=0.10$. Multiply independent probabilities for joint occurrence.

7. What is the definition of a simulation in probability for a compound event?

   A model using random trials to estimate a compound event's probability. Uses randomness to mimic real-world compound events.

8. What is the multiplication rule for independent events $A$ and $B$?

   $P(A \text{ and } B)=P(A)\cdot P(B)$. Multiply individual probabilities when events don't affect each other.

9. If $P(A)=0.2$ and $P(B)=0.3$ are mutually exclusive, what is $P(A \text{ or } B)$?

   $0.2+0.3=0.5$. Add probabilities when events can't occur together.

10. If $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{2}$ are independent, what is $P(A \text{ and } B)$?

    $\frac{1}{3}\cdot\frac{1}{2}=\frac{1}{6}$. Multiply fractions for independent events happening together.

11. Identify the probability model for simulating "donor has type A blood" if $P(A)=0.40$.

    Use $10$ digits; let $0$–$3$ mean type A and $4$–$9$ mean not A. $4$ of $10$ digits represents $0.40$ probability.

12. What is the probability a simulated donor is not type A if $P(\text{A})=0.24$?

    $1-0.24=0.76$. Complement rule: subtract from $1$ for "not" events.

13. What is the relative frequency of an event in a simulation?

    $\frac{\text{number of successes}}{\text{total trials}}$. Counts successes divided by total attempts in the experiment.

14. What is the expected number of successes in $n$ trials if $P(\text{success})=p$?

    $n\times p$. Multiply trials by probability for expected successes.

15. What is the definition of a compound event?

    An event made from two or more simple events. Combines multiple simple events into one outcome.

16. What is the estimated probability if a simulation has $18$ successes in $60$ trials?

    $\frac{18}{60}=0.3$. Divide successes by total trials to get experimental probability.

17. What is the definition of experimental probability from a simulation?

    $\frac{\text{number of successes}}{\text{number of trials}}$. Ratio of favorable outcomes to total attempts.

18. What is the expected number of trials to get one success if $P(\text{success})=0.2$?

    $\frac{1}{0.2}=5$. Expected trials equals $1$ divided by success probability.

19. What is one correct way to simulate a probability of $\frac{3}{8}$ using equally likely outcomes?

    Use $8$ equally likely outcomes; mark $3$ as "success". $\frac{3}{8}$ requires $3$ successes out of $8$ total outcomes.

20. Which option best represents a fair simulation for $P(A)=\frac{1}{4}$ using cards?

    Use $4$ equally likely cards; label $1$ card as success. $1$ out of $4$ cards gives $25\%$ chance, matching the probability.

21. What is the addition rule for mutually exclusive events $A$ and $B$?

    $P(A \text{ or } B)=P(A)+P(B)$. Add probabilities when events can't happen simultaneously.

22. If $P(A)=0.4$ and $P(B)=0.5$ are independent, what is $P(A \text{ and } B)$?

    $0.4\cdot 0.5=0.2$. Multiply probabilities for independent events occurring together.

23. In a simulation, what is one trial when modeling "donor is type A and Rh$+$"?

    One randomly generated donor outcome for both blood type and Rh factor. Each trial tests both characteristics of one donor.

24. Identify the correct multiplication rule for independent events $A$ and $B$.

    $P(A\text{ and }B)=P(A)\times P(B)$. Independent events multiply their individual probabilities.

25. If $P(\text{type A})=0.40$, what is the expected number of type A donors in $50$ trials?

    $50\times 0.40=20$. Expected value = trials × probability of success.

26. What does it mean for two events to be independent in a simulation?

    One event's outcome does not change the other's probability. Like flipping two coins - first flip doesn't affect second.

27. If events $A$ and $B$ are mutually exclusive with $P(A)=0.35$ and $P(B)=0.25$, what is $P(A\text{ or }B)$?

    $0.35+0.25=0.60$. Add probabilities when events can't happen together.

28. If $P(\text{type A})=0.40$, what is the expected number of donors needed to find $1$ type A donor?

    $\frac{1}{0.40}=2.5$. Average trials needed = $\frac{1}{\text{probability}}$.

29. What is the expected number of trials to get $1$ success if $P(\text{success})=p$?

    $\frac{1}{p}$. Reciprocal of probability gives expected trials.

30. In $200$ trials, "A then B" occurred $46$ times. What is the relative frequency?

    $\frac{46}{200}=0.23$. Frequency divided by total trials gives relative frequency.

31. What does it mean if simulation results stabilize as trials increase?

    The relative frequency is approaching the true probability. Law of large numbers: more trials yield better estimates.

32. What is the experimental probability (estimate) after a simulation?

    The event's relative frequency from the trials. The simulation's success rate approximates the true probability.

33. Which option best represents a fair simulation for $P(A)=0.3$ using digits?

    Use digits $0$–$9$; let $0,1,2$ represent event $A$. $3$ of $10$ digits gives $30\%$ chance, matching the probability.

34. What is the expected number of trials to get one success if $P(\text{success})=\frac{1}{8}$?

    $\frac{1}{\frac{1}{8}}=8$. Reciprocal of probability gives expected trials to first success.

35. What is the estimated probability of success if $12$ of $50$ simulated donors have type A?

    $\frac{12}{50}=0.24$. Divide type A donors by total donors tested.

36. What is the definition of relative frequency in a simulation?

    $\frac{\text{frequency of an outcome}}{\text{total trials}}$. Shows how often an outcome occurs proportionally.

37. Identify the correct addition rule for mutually exclusive events $A$ and $B$.

    $P(A\text{ or }B)=P(A)+P(B)$. Mutually exclusive events can't occur together, so add.

38. What is the experimental probability if $18$ successes occur in $60$ simulation trials?

    $\frac{18}{60}=0.30$. Divide successes by total trials for experimental probability.

39. What is the estimated probability if a simulation has $27$ successes in $90$ trials?

    $\frac{27}{90}=0.3$. Simplifies to $\frac{3}{10}$ or $30\%$ success rate.

40. Identify the correct simulation tool for $P(A)=\frac{2}{5}$ using a spinner.

    A spinner with $5$ equal sections, with $2$ labeled success. $2$ out of $5$ sections gives $40\%$ chance, matching the probability.

Study these flashcards