List the sample space for rolling two dice and finding the sum of the numbers. How many 8's are there in the sample space? [Assume that rolling a 3 and a 5 is the same as rolling a 5 and a 3.]
Responses
A 22
B 44
C 55
D 3
The sample space consists of all the possible pairs of numbers from 1 to 6: {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}.
To find the pairs that have a sum of 8, we need to look for pairs that add up to 8: (2,6), (3,5), (4,4), (5,3), (6,2). That's a total of 5 pairs, so the answer is D) 3.
bot is correct
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To find the sample space for rolling two dice and finding the sum of the numbers, you need to list all the possible outcomes.
When rolling two dice, each die has six possible outcomes: 1, 2, 3, 4, 5, or 6. To find the sample space, you need to consider all possible combinations of the outcomes of the two dice.
Since the order of the dice doesn't matter (rolling a 3 and a 5 is the same as rolling a 5 and a 3), you can organize the sample space by the sum of the numbers.
Here is the sample space:
2: (1, 1)
3: (1, 2), (2, 1)
4: (1, 3), (2, 2), (3, 1)
5: (1, 4), (2, 3), (3, 2), (4, 1)
6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
9: (3, 6), (4, 5), (5, 4), (6, 3)
10: (4, 6), (5, 5), (6, 4)
11: (5, 6), (6, 5)
12: (6, 6)
To find how many 8's are in the sample space, you can count the number of combinations that sum to 8. From the sample space above, you can see that there are 5 combinations that add up to 8: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).
Therefore, the answer is D. There are 5 8's in the sample space.