Question 6
Provide an appropriate response.
A single die is rolled twice. The set of 36 equally likely outcomes is $\{(1,1),(1,2),(1,3),(1,4),(1,5)$, $(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3)$, $(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$. Find the probability of getting two numbers whose sum is greater than 9 and less than 13 .
0
$\frac{7}{36}$
$\frac{5}{36}$
$\frac{1}{6}$

Step 1 ：A single die is rolled twice, resulting in a set of 36 equally likely outcomes.

Step 2 ：We are looking for the outcomes where the sum of the two numbers rolled is greater than 9 and less than 13.

Step 3 ：The outcomes that satisfy this condition are (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6).

Step 4 ：Since there are 6 possible outcomes for each roll, there are a total of \(6*6 = 36\) possible outcomes.

Step 5 ：The event of getting a sum greater than 9 and less than 13 occurs in 6 of these outcomes.

Step 6 ：Therefore, the probability of this event is \(\frac{6}{36}\), which simplifies to \(\frac{1}{6}\).

Step 7 ：Final Answer: The probability of getting two numbers whose sum is greater than 9 and less than 13 when rolling a die twice is \(\boxed{\frac{1}{6}}\).