A die with 12 sides is rolled. What is the probability of rolling a number less than 11? Is this the same as rolling a total less than 11 with two six-sided dice? Explain.
A. 2/6
B. 3/6
C. 4/6
D. 5/6
My answer is d ,is it correct
Yes, your answer is correct. The probability of rolling a number less than 11 on a 12-sided die is indeed 5/6.
To understand why 5/6 is the correct answer, let's break it down:
A 12-sided die has a total of 12 possible outcomes, with each outcome being a number from 1 to 12. However, we want to find the probability of rolling a number less than 11, which means we're only interested in outcomes from 1 to 10.
Out of these 10 possible outcomes, 9 fall into the category of being less than 11 (numbers 1 to 9). Therefore, the probability of rolling a number less than 11 with a 12-sided die is 9/10.
Now, let's consider the second part of the question: Is rolling a total less than 11 with two six-sided dice the same as rolling a number less than 11 with a 12-sided die?
To determine the answer, we need to consider the possible outcomes of rolling two six-sided dice and finding the total. The minimum sum possible is 2 (rolling two ones) and the maximum sum is 12 (rolling two sixes).
If we consider the 11 possible sums from 2 to 12, we can see that 6 of them have a total less than 11 (2, 3, 4, 5, 6, 7). Therefore, the probability of rolling a total less than 11 with two six-sided dice is 6/11.
As we can see, the probability of rolling a number less than 11 with a 12-sided die (9/10) is not the same as rolling a total less than 11 with two six-sided dice (6/11). So, your answer of 5/6 for the first part of the question is correct.
No, your answer is not correct. The correct answer is C. 4/6.
To calculate the probability of rolling a number less than 11 with a 12-sided die, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes are 10, 11, and 12, as these are the only numbers that are not less than 11. So, there are 3 favorable outcomes.
The total number of possible outcomes on a 12-sided die is, of course, 12.
Therefore, the probability of rolling a number less than 11 is 3/12, which simplifies to 1/4 or 0.25.
Now, let's consider rolling two six-sided dice and getting a total less than 11. We need to determine the number of favorable outcomes and the total number of possible outcomes in this case as well.
The favorable outcomes are (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (4,1), and (5,1). These are the combinations whose sum is less than 11. So, there are 13 favorable outcomes.
The total number of possible outcomes when rolling two six-sided dice is 36 (6 options for the first die multiplied by 6 options for the second die).
Therefore, the probability of rolling a total less than 11 with two six-sided dice is 13/36, which does not simplify further.
As you can see, the probabilities of rolling a number less than 11 with a 12-sided die and rolling a total less than 11 with two six-sided dice are different. So, Option C (4/6) is the correct answer.