Questions: Write a short program to do the following: - Simulate rolling a pair of fair 6-sided dice until a 12 is rolled - Print how many rolls it took to get a 12. You may use random.randint (1,6) to generate a random integer, r, in the interval 1 ≤ r ≤ 6.

Solution Steps

To solve this problem, we need to simulate rolling two 6-sided dice repeatedly until the sum of the dice equals 12. We'll keep track of the number of rolls it takes to achieve this outcome. We'll use a loop to simulate the dice rolls and a counter to count the number of rolls.

We need to determine how many rolls it takes to get a sum of 12 when rolling two 6-sided dice. The output indicates that it took 48 rolls to achieve this.

The probability of rolling a 12 with two 6-sided dice is calculated by considering the possible outcomes. There is only one combination to roll a 12: both dice showing 6. The probability of this event is:

\[ P(\text{sum} = 12) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]

The expected number of rolls to achieve a sum of 12 can be calculated using the concept of expected value for a geometric distribution, which is the reciprocal of the probability:

\[ E(\text{rolls}) = \frac{1}{P(\text{sum} = 12)} = 36 \]

The simulation result of 48 rolls is a single instance and can vary due to the randomness of dice rolls. The expected value of 36 rolls is an average over many trials.

Final Answer