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Lesson · Grade 10 · Workplace Mathematics

Simulating a game to estimate a probability

  • Grade 10
  • Workplace Mathematics
  • 2 min 2 s
  • British Columbia
  • BC10-MA-60

One roll of a fair die stands for one cereal box with one of 6 equally likely cards. The video plans the simulation (one trial: roll until all six numbers have appeared, record the rolls, run 20 trials), runs trial 1 roll by roll (11 rolls), fast-forwards 19 more and averages them: 296 ÷ 20 = 14.8, about 15 boxes, with an experimental probability of 3/20 = 0.15 of needing more than 20. It warns that too few trials mislead, because the first 5 average only 11, while thousands of trials settle near 14.7, and it ends on a one-line recap.

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In one sentence

The question this lesson answers

Each cereal box holds one of 6 cards, all equally likely. How many boxes until you have all 6?

A simulation copies a chance process using something simpler that behaves the same way.

Transcript

What the lesson says

Each cereal box holds one of 6 cards, all equally likely. How many boxes until you have all 6?

A simulation copies a chance process using something simpler that behaves the same way.

A fair die has 6 equally likely numbers, so one roll stands for one box, and the number rolled is the card inside.

First, plan it. One trial means rolling until all six numbers have appeared.

Record how many rolls each trial took, and run 20 trials.

Trial 1. Each new number is ticked off, and repeats still count as rolls.

The last missing number, 3, comes up on roll 11, so trial 1 took 11 rolls.

Here are the other 19 trials, fast-forwarded. Each one is run the same way.

Adding all 20 results gives a total of 296.

The mean is the total divided by the number of trials: 296 divided by 20 is 14.8, or about 15 boxes.

Experimental probability is the number of trials where an event happens, divided by the total number of trials.

3 trials needed more than 20 boxes: 22, 27 and 21. So that probability is 3 out of 20, or 0.15.

A common mistake is trusting too few trials. Our first 5 have a mean of just 11, and none needed more than 20.

More trials give a more reliable estimate. Over thousands of trials, the mean settles near 14.7.

Plan one trial, record each result, run many trials, then find the mean or the probability.

Curriculum

Where this fits

British Columbia, Grade 10

Workplace Mathematics 10, Data and probability: experimental probabilityBC10-MA-60

Previous: Range and Outliers: How One Late Delivery Changes the MeasuresNext: Simulation vs Theory: Rolling a Sum of 7

The outcomes and strands follow the British Columbia curriculum.

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