2. Two fair dice are rolled at the same time and the number of dots appearing on both dice is counted. Find the probability that the sum is
A. 7
B. is an odd number greater than 6
C. is less than 2
D. Is more than 12
E. Is "Snake Eyes"
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A. How many different ways can you get 7 with two dice?
6,1
1,6
5,2
2,5
3,4
4,3
Divide that by the total number of possible alternatives.
B. What odd numbers that can be obtained are greater than 6? (7, 9, 11) How many ways can they be obtained? Divide that by the total number of possible alternatives.
C and D have the same answer.
E. How many ways can you obtain "snake eyes"?Divide that by the total number of possible alternatives.
This should give you a start.
To find the probability of each event, we need to first determine the total number of possible outcomes.
There are 6 possible outcomes for the roll of each die (1, 2, 3, 4, 5, 6). Since there are 2 dice, the total number of possible outcomes is 6 * 6 = 36.
A. To find the probability that the sum is 7, we need to count the number of outcomes where the sum is 7. There are 6 possible outcomes with a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). So the probability is 6/36 = 1/6.
B. To find the probability that the sum is an odd number greater than 6, we need to count the number of outcomes that meet this condition. The possible odd numbers greater than 6 from the sum of two dice are 7 and 9. There are 6 possible outcomes with a sum of 7 and only 1 possible outcome with a sum of 9: (3, 6). So the probability is 7/36.
C. To find the probability that the sum is less than 2, we need to count the number of outcomes where the sum is less than 2. Since the minimum sum possible is 1, there are no possible outcomes with a sum less than 2. So the probability is 0/36 = 0.
D. To find the probability that the sum is more than 12, we need to count the number of outcomes where the sum is more than 12. Since the maximum sum possible is 12, there are no possible outcomes with a sum more than 12. So the probability is 0/36 = 0.
E. To find the probability that the sum is "Snake Eyes" (both dice show a 1), we need to count the number of outcomes where both dice show a 1. There is only 1 possible outcome with a sum of "Snake Eyes" (1, 1). So the probability is 1/36.
Summary:
A. The probability that the sum is 7 is 1/6.
B. The probability that the sum is an odd number greater than 6 is 7/36.
C. The probability that the sum is less than 2 is 0.
D. The probability that the sum is more than 12 is 0.
E. The probability that the sum is "Snake Eyes" is 1/36.
To find the probability for each of the given scenarios, we need to first determine the total number of possible outcomes and then count the favorable outcomes for each scenario.
1. Total number of possible outcomes: When two fair dice are rolled simultaneously, each die has 6 possible outcomes (from 1 to 6). So, the total number of possible outcomes is 6 * 6 = 36.
Now, let's calculate the favorable outcomes for each scenario:
A. The sum is 7: To get a sum of 7, the possible outcomes are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So, there are 6 favorable outcomes.
B. The sum is an odd number greater than 6: The possible outcomes are (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 3), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5). So, there are 16 favorable outcomes.
C. The sum is less than 2: There is no possible outcome where the sum is less than 2. So, there are 0 favorable outcomes.
D. The sum is more than 12: There is no possible outcome where the sum is more than 12. So, there are 0 favorable outcomes.
E. "Snake Eyes" refers to rolling two dice and getting a sum of 2. So, there is only one favorable outcome, which is (1, 1).
Now, we can calculate the probabilities:
A. Probability of getting a sum of 7 = (Number of favorable outcomes) / (Total number of possible outcomes) = 6 / 36 = 1/6.
B. Probability of getting an odd sum greater than 6 = 16 / 36 = 4/9.
C. Probability of getting a sum less than 2 = 0 / 36 = 0.
D. Probability of getting a sum more than 12 = 0 / 36 = 0.
E. Probability of getting "Snake Eyes" = 1 / 36.