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Design a Simulation

Say what one trial is, how you read it, then divide successes by trials.

ExampleA cereal box contains one of 4 equally likely prizes. You want to estimate the probability of getting all 4 different prizes in 4 boxes.
Describe a simulation using a four-sided die (or a spinner with 4 equal parts): say what one trial is and how you would read the result. Then, if 20 trials gave 5 successes, what is your estimate? Design: one roll = one box, and the number rolled = which prize. One trial is a complete set of those, and you record whether all 4 different prizes in 4 boxes happened. Repeat the trial many times.
Estimate: 5 successes ÷ 20 trials = 14 ≈ 25%.
This is an estimate, not the exact probability — a different 20 trials would give a different answer. More trials narrow the spread, which is why a simulation is worth running many times rather than once.
  1. 1.A cereal box contains one of 4 equally likely prizes. You want to estimate the probability of getting all 4 different prizes in 4 boxes.
    Describe a simulation using a four-sided die (or a spinner with 4 equal parts): say what one trial is and how you would read the result. Then, if 20 trials gave 7 successes, what is your estimate?
  2. 2.A bus is late on 1 day in 3. You want to estimate the probability of getting the bus late on both of the next 2 days.
    Describe a simulation using a die: say what one trial is and how you would read the result. Then, if 40 trials gave 7 successes, what is your estimate?
  3. 3.A basketball player makes 50% of her free throws. You want to estimate the probability of getting at least 3 of her next 4 shots.
    Describe a simulation using a coin: say what one trial is and how you would read the result. Then, if 20 trials gave 5 successes, what is your estimate?
  4. 4.A quiz has 5 true/false questions and a student guesses every one. You want to estimate the probability of getting at least 4 correct by guessing.
    Describe a simulation using a coin: say what one trial is and how you would read the result. Then, if 40 trials gave 4 successes, what is your estimate?
  5. 5.A basketball player makes 50% of her free throws. You want to estimate the probability of getting at least 3 of her next 4 shots.
    Describe a simulation using a coin: say what one trial is and how you would read the result. Then, if 30 trials gave 6 successes, what is your estimate?