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Course: Statistics and probability > Unit 7

Lesson 5: Randomness, probability, and simulation
Math
Statistics and probability
Probability
Randomness, probability, and simulation
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Theoretical and experimental probability: Coin flips and die rolls

Google Classroom
Probability tells us how likely something is to happen in the long run. We can calculate probability by looking at the outcomes of an experiment or by reasoning about the possible outcomes.

Part 1: Flipping a coin

question a
A fair coin has 2 sides (heads and tails) that are equally likely to show when the coin is flipped.
What is the theoretical probability that a fair coin lands on heads?
P(heads)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

question b
Dave flipped a coin 20 times and got heads on 8 of the flips.
Based on Dave's results, what is the experimental probability of the coin landing on heads?
P(heads)≈
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

question c
Why aren't the theoretical and experimental results the same?
صرف 1 جواب چنو

question d
Dave continues flipping his coin until he has 100 total flips, and the coin shows heads on 47 of those flips.
Based on these results, what is the experimental probability of the coin landing on heads?
P(heads)≈
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

question e
What do you notice about the experimental probability after Dave continued flipping the coin?
صرف 1 جواب چنو

Part 2: Rolling a die

question a
A fair die has 6 faces numbered 1 through 6 that are each equally likely to show when the die is rolled.
What is the theoretical probability that a fair die shows a 1?
P(1)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

question b
Dave is going to roll a die 60 times and see how often a 1 shows.
According to the theoretical probability, how many rolls should Dave expect to show a 1?
≈
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
rolls

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