Answer: 0.0972
Explanation:
To find the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10, we need to find the probabilities of each event separately and then multiply them together.
First, let's find the probability of the first roll being a total of at least 7. There are a total of 36 possible outcomes when rolling a pair of dice (6 sides on each die, so 6 x 6 = 36). To get a total of at least 7, the following outcomes are possible:
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)
There are 21 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 7 in the first roll is:
P(at least 7) = 21/36
Next, let's find the probability of the second roll being a total of at least 10. The following outcomes are possible:
10: (4, 6), (5, 5), (6, 4)
11: (5, 6), (6, 5)
12: (6, 6)
There are 6 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 10 in the second roll is:
P(at least 10) = 6/36
Now, to find the probability that both events happen, we multiply the probabilities of each event:
P(first roll at least 7 and second roll at least 10) = P(at least 7) * P(at least 10) = (21/36) * (6/36)
P(first roll at least 7 and second roll at least 10) = 126/1296
So, the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10 is 126/1296, or approximately 0.0972 (rounded to four decimal places).