Probability Simulations - Pre Algebra

1. What is one trial in a simulation?

   One complete run of the modeled situation, such as flipping 4 coins once to model one family of 4 children.

2. How does running more trials affect a simulation's estimate of a probability?

   The estimate tends to get closer to the true (theoretical) probability as the number of trials grows.

3. A fair number cube simulates an event with probability $\frac{1}{3}$. How many faces should represent success?

   2 faces. $\frac{2}{6} = \frac{1}{3}$.

4. A simulation of 4 coin flips is run 80 times, and at least 3 heads occur in 25 of the runs. What is the experimental probability?

   $\frac{5}{16}$ (0.3125). $\frac{25}{80} = \frac{5}{16}$.

5. What must be true about the chance device for a simulation to be valid?

   The probabilities of its outcomes must match the probabilities of the real event being modeled.

6. How is an estimated (experimental) probability found from a simulation?

   Divide the number of trials in which the event happened by the total number of trials.

7. In 50 simulated spins, a spinner landed on red 35 times. Based on this, about how many reds should be expected in 400 spins?

   About 280. The estimated probability is $\frac{35}{50} = 0.7$, and $0.7 \times 400 = 280$.

8. Random two-digit numbers 00 to 99 simulate an event with probability $0.25$. How many of the numbers should represent success?

   25. There are 100 equally likely numbers, and $0.25 \times 100 = 25$.

9. Random digits 0 through 9 simulate an event with probability $0.3$. How many of the ten digits should represent success?

   3 digits. Each digit has probability $0.1$, so 3 digits give $0.3$.

10. A simulation runs 200 trials, and the event happens in 46 of them. What is the estimated probability?

    $0.23$. $\frac{46}{200} = 0.23$.

11. What is a probability simulation?

    A model that uses a chance device, such as a coin, number cube or random numbers, to imitate a real event and estimate its probability.

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