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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 number cube (assuming it is fair and has six equally likely outcomes) is 1/6.
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 came up by the total number of rolls.
experimental probability of rolling a 3 = 67/450
This fraction cannot be simplified further.
Answer the question and make it make sense. 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.
If you roll a number cube 450 times, the number 3 comes up 67 times. To determine the probability of rolling a 3, we can calculate the theoretical probability and the experimental probability. The theoretical probability of rolling a 3 on a fair number cube is 1/6, since there are 6 equally likely outcomes. The experimental probability of rolling a 3 is 67/450, which we get by dividing the number of times a 3 came up (67) by the total number of rolls (450). The experimental probability is an approximation based on actual data, while the theoretical probability is based on probability theory. Both probabilities can be expressed as fractions in simplest form.
a. To find the theoretical probability of rolling a 3, we divide the number of favorable outcomes (the number of times a 3 can come up) by 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 number of favorable outcomes is 67.
The total number of possible outcomes when rolling a number cube is 6, because the cube has 6 faces numbered from 1 to 6.
Therefore, the theoretical probability of rolling a 3 is 67/450.
b. To find the experimental probability of rolling a 3, we divide the number of times the event occurred (in this case, rolling a 3) by the total number of trials.
In this case, the number cube was rolled 450 times and the number 3 came up 67 times. So, the number of times the event occurred is 67.
Therefore, the experimental probability of rolling a 3 is 67/450.