You conduct an experiment of dice rolling and roll a six 14 times out of 56 rolls. Write both the experimental probability and the theoretical probability in fraction and percent form.
Experimental: 14/56 = 1/4 = 25%
Theoretical: 6/56 = 3/28 = 10.71%
To find the experimental probability, divide the number of times an event occurs by the total number of trials. In this case, the event is rolling a six, which occurred 14 times out of 56 rolls.
Experimental Probability:
- Fraction form: 14/56
- Percent form: (14/56) * 100 = 25%
Theoretical probability is calculated based on the assumption of equal likelihood for each possible outcome. Since a fair die has six sides, each with an equal chance of landing, the theoretical probability of rolling a six is 1/6.
Theoretical Probability:
- Fraction form: 1/6
- Percent form: (1/6) * 100 = 16.67%
To find the experimental probability, you would divide the number of times the desired outcome occurred (rolling a six) by the total number of trials (56 rolls).
Experimental probability (fraction):
Number of times rolling a six = 14
Total number of rolls = 56
14/56
To simplify this fraction, both the numerator and the denominator can be divided by 14:
1/4
Experimental probability (percent):
To convert the fraction to a percentage, divide the numerator by the denominator and multiply by 100.
(1/4) * 100 = 25%
Now let's find the theoretical probability. Since you are rolling a fair six-sided die, there is an equal chance of rolling any number from 1 to 6.
Theoretical probability (fraction):
The total number of outcomes is 6 (since there are 6 possible numbers on a die), and the desired outcome is rolling a six.
1/6
Theoretical probability (percent):
To convert the fraction to a percentage, divide the numerator by the denominator and multiply by 100.
(1/6) * 100 = 16.67%
So the experimental probability of rolling a six is 1/4 or 25% while the theoretical probability is 1/6 or approximately 16.67%.