1. The probability of rolling a five on a single die is 1/6. Since the two rolls are independent, the probability of rolling a five twice is (1/6) * (1/6) = 1/36.
2. The numbers less than 5 on a die are 1, 2, 3, and 4, so the probability of rolling a number less than 5 is 4/6 = 2/3. The numbers more than 2 on a die are 3, 4, 5, and 6, so the probability of rolling a number more than 2 is 4/6 = 2/3. Since the rolls are independent, the combined probability is (2/3) * (2/3) = 4/9.
3. The probability of rolling a one on a single die is 1/6. Since the two rolls are independent, the probability of rolling two ones is (1/6) * (1/6) = 1/36.
4. A standard die has faces numbered 1 through 6. It is impossible to roll a 7. Therefore, the probability of rolling a 1 and then a 7 is 0.
5. The probability of rolling any number between 1 and 6 on the first roll is 6/6 = 1. For the second roll, you need a different number, so there are 5 possible outcomes out of 6. The probability for the second roll is 5/6. Since the rolls are independent, the combined probability is 1 * (5/6) = 5/6.
Parent Tip: Review the logic above to help your child master the concept of statistic and probability worksheet.
