Final answer:
The probability of rolling 2 sixes in a row is 1/36 or 2.7778%. The probability of rolling 2 ones in a row is also 1/36 or 2.7778%. The probability of getting a total of 7 on two rolls is 1/6 or approximately 16.6667%. The probability of getting a 1 OR a 5 is 11%. The probability of rolling a 3 on one roll and a 2 on the next roll is 680.4%.
Step-by-step explanation:
Probability of Rolling 2 Sixes in a Row
The probability of rolling a six on a fair, six-sided die is 1/6. Since each roll is independent, the probability of rolling two sixes in a row is (1/6) * (1/6) = 1/36. To express this as a percentage, we convert the fraction to a decimal and then multiply by 100: (1/36) * 100 = 2.7778%
Probability of 2 Ones in a Row
Similarly, the probability of rolling a one on a fair, six-sided die is 1/6. Therefore, the probability of rolling two ones in a row is (1/6) * (1/6) = 1/36. Converting this to a percentage, we get 2.7778%.
Probability of a Total of 7 on Two Rolls
There are 6 possible outcomes on each roll, and 2 rolls are made. So, the total number of outcomes is 6 * 6 = 36. Out of these, there are 6 ways to get a total of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Therefore, the probability of getting a total of 7 on two rolls is 6/36 = 1/6, which is approximately 16.6667%.
Probability of Getting a 1 OR a 5
Out of the 1000 rolls, the frequency of getting a 1 is 19 and the frequency of getting a 5 is 91. To calculate the probability of getting a 1 or a 5, we add these frequencies together: 19 + 91 = 110. Then, we divide this by the total number of rolls (1000) and multiply by 100 to express it as a percentage: (110/1000) * 100 = 11%
Probability of Rolling a 3 and then a 2
Out of the 1000 rolls, the frequency of getting a 3 is 84 and the frequency of getting a 2 is 81. To calculate the probability of rolling a 3 on one roll and a 2 on the next roll, we multiply these frequencies together: 84 * 81 = 6804. Then, we divide this by the total number of rolls (1000) and multiply by 100 to express it as a percentage: (6804/1000) * 100 = 680.4%