A number cube is rolled 450 times. The number 3 comes up 67 times.
What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
surely that would be 1/6
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.
a. The theoretical probability of rolling a 3 on a fair number cube is 1/6, since there are six equally likely outcomes (numbers 1 through 6) and one of them is a 3. Therefore, the theoretical probability of rolling a 3 is 1/6.
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 came up (67) by the total number of rolls (450). So the experimental probability of rolling a 3 is 67/450, which can be simplified to 149/1000.
To find the theoretical probability of rolling a 3 on a number cube, we need to calculate the ratio of the favorable outcomes (rolling a 3) to the total number of possible outcomes.
In this case, the number cube is rolled 450 times, and the number 3 comes up 67 times. So, the favorable outcome is rolling a 3, which occurred 67 times.
The total number of possible outcomes when rolling a number cube is 6, since there are 6 sides numbered from 1 to 6.
Therefore, the theoretical probability of rolling a 3 can be calculated as:
P(rolling a 3) = Number of favorable outcomes / Total number of possible outcomes
= 67 / 450
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case because 67 and 450 share no common factors other than 1.
Therefore, the simplified fraction is:
P(rolling a 3) = 67/450
So, the theoretical probability of rolling a 3 is 67/450.