A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
450 / 6 = 75
a. = 1/6
b. 67/450 =
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To find the theoretical probability, we need to determine the ratio of the number of favorable outcomes (rolling a 3) to the total number of possible outcomes (rolling the number cube 450 times).
a. The number cube has 6 sides, so it has 6 possible outcomes (numbers 1 to 6). The number 3 is one of these possible outcomes, so the ratio of favorable outcomes to total outcomes is 1 to 6. Therefore, the theoretical probability of rolling a 3 is 1/6.
To find the experimental probability, we need to calculate the ratio of the number of times the favorable outcome occurs (rolling a 3) to the total number of trials (rolling the number cube 450 times).
b. In this case, the number 3 was rolled 67 times out of 450, so the ratio of favorable outcomes to total outcomes is 67 to 450. We can simplify this fraction by dividing both numerator and denominator by their greatest common divisor, which is 1. Therefore, the experimental probability of rolling a 3 is 67/450.