1. The experimental probability of rolling an even number is calculated by dividing the total frequency of even numbers by the total number of rolls. Even numbers on a cube are 2, 4, and 6. From the table: Frequency of 2 = 3, Frequency of 4 = 8, Frequency of 6 = 7. Total frequency of even numbers = 3 + 8 + 7 = 18. Total rolls = 8 (for 1) + 3 (for 2) + 9 (for 3) + 8 (for 4) + 5 (for 5) + 7 (for 6) = 40. Experimental probability = 18 / 40 = 0.45 or 45%.
2. The experimental probability of rolling an even number was 0.45 (from question 1). If you roll the cube 36 times, you would expect to roll an even number 0.45 * 36 = 16.2 times. Since you can't roll a fraction of a time, you would expect approximately 16 times.
3. From the table, the frequency for rolling the number one is 8. So, you rolled the number one 8 times in the experiment.
4. The theoretical probability of rolling a number greater than 4 is the probability of rolling a 5 or a 6. There are 2 favorable outcomes (5 and 6) out of 6 possible outcomes. Theoretical probability = 2 / 6 = 1/3 ≈ 0.333 or 33.3%.
5. The experimental probability of rolling a number greater than 4 is calculated from the table. Numbers greater than 4 are 5 and 6. Frequency of 5 = 5, Frequency of 6 = 7. Total frequency for numbers > 4 = 5 + 7 = 12. Total rolls = 40. Experimental probability = 12 / 40 = 0.3 or 30%.
6. The difference between theoretical and experimental probability is |Theoretical Probability - Experimental Probability| = |1/3 - 0.3| = |0.333... - 0.3| = 0.033... or approximately 0.033.
7. If a car factory checks 360 cars and 8 of them have defects, the defect rate is 8 / 360 = 1/45. For 1260 cars, the expected number of defective cars is (1/45) * 1260 = 28.
Parent Tip: Review the logic above to help your child master the concept of theoretical and experimental probability worksheet.
