Question

A number cube is rolled 500 times. Here are the results: Outcome Rolled 1 2 3 4 5 6 Calculate the following probabilities to the nearest thousandth. The theoretical probability of rolling a 5 or 6 The experimental probability of rolling a 5 or 6 [Choose ] Number of Rolls 81 95 79 89 80 76 [Choose]​

Answer 1

The theoretical probability of rolling a 5 or 6 can be calculated by finding the sum of the probabilities of rolling a 5 and rolling a 6. Since the number cube has 6 equally likely outcomes, the probability of rolling a 5 or 6 is:

Theoretical probability = (probability of rolling a 5) + (probability of rolling a 6)

= 1/6 + 1/6

= 2/6

= 1/3

The experimental probability of rolling a 5 or 6 can be calculated by dividing the number of times a 5 or 6 was rolled by the total number of rolls. From the given data, the number of rolls for each outcome is:

Outcome | Number of Rolls

1 | 81

2 | 95

3 | 79

4 | 89

5 | 80

6 | 76

Experimental probability = (number of times a 5 or 6 was rolled) / (total number of rolls)

= (number of times a 5 was rolled + number of times a 6 was rolled) / 500

= (80 + 76) / 500

= 156 / 500

= 0.312

Therefore, the theoretical probability of rolling a 5 or 6 is 1/3, and the experimental probability is approximately 0.312.

Explanation: