probability · Year 6 · AC9M6P02
Experimental and theoretical probability
Theoretical probability comes from counting equally likely outcomes. Experimental probability comes from what actually happened: the number of times the event happened over the number of trials. To predict, multiply the theoretical probability by the number of trials: a fair dice rolled 60 times should give about 60 ÷ 6 = 10 sixes. Real results wobble around the expected number, and the wobble matters less when there are more trials.
Sample questions
Omar rolled a standard dice 60 times. A six came up 44 times. What was the experimental probability of a six?
- Experimental probability uses the results, not the theory.
- A six happened 44 times out of 60 trials.
- Experimental probability = 44/60 = 11/15.
Answer: 11/15
Ella tossed a coin 30 times. It landed on heads 23 times. What was the experimental probability of heads?
- Experimental probability uses the results, not the theory.
- Heads happened 23 times out of 30 trials.
- Experimental probability = 23/30.
Answer: 23/30
Ella tossed a coin 30 times. It landed on heads 14 times. What was the experimental probability of heads?
- Experimental probability uses the results, not the theory.
- Heads happened 14 times out of 30 trials.
- Experimental probability = 14/30 = 7/15.
Answer: 7/15