Lesson · Grade 5 · Mathematics
Experimental and Theoretical Probability: Flip a Coin, Roll a Die
- Grade 5
- Mathematics
- 1 min 16 s
- British Columbia
- BC5-MA-37
A coin and a die are independent events, and a table of their 12 equally likely outcomes shows that heads with an even number has a theoretical probability of 3/12 = 1/4 = 25%. The coin and die are then tried 40 times, with each result counted in the table: heads with an even number came up 12 times, an experimental probability of 12/40 = 30%, which is close to 25% but not the same, and more trials usually bring the two closer.
Concept: Experimental and theoretical probability
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In one sentence
The question this lesson answers
If we flip a coin and roll a die, how likely is heads with an even number?
The coin cannot change the die, so these are independent events.
Transcript
What the lesson says
If we flip a coin and roll a die, how likely is heads with an even number?
The coin cannot change the die, so these are independent events.
A table shows all 2 times 6, or 12, outcomes, and each one is equally likely.
Heads with a 2, a 4 or a 6 are the 3 outcomes out of 12 that match.
The theoretical probability is 3 out of 12, which is one quarter, or 25 percent.
Now we really flip and roll 40 times and count every result.
Heads with an even number came up 5 plus 3 plus 4, which is 12 times.
The experimental probability is 12 out of 40, which is three tenths, or 30 percent.
25 percent and 30 percent are close, but they are not the same.
With more trials, the experimental probability usually gets closer to the theoretical one.
Theoretical probability is what we expect, and experimental probability is what really happened.
Curriculum
Where this fits
- British Columbia, Grade 5
Mathematics, Data and probability: probability experiments, single events or outcomesBC5-MA-37
- British Columbia, Grade 6
Mathematics, Data and probability: single-outcome probability, both theoretical and experimentalBC6-MA-45
- British Columbia, Grade 7
Mathematics, Data and probability: experimental probability with two independent eventsBC7-MA-67
Previous: Drawing a circle graph from dataNext: What Independent Events Are
This lesson is also listed in Grade 6 and Grade 7.
The outcomes and strands follow the British Columbia curriculum.
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