What is the probability of rolling a one on the first die and a one on the second die?
The probability of rolling a one on a fair six-sided die is 1/6. Since the two dice are independent events, the probability of rolling a one on both dice is the product of the individual probabilities. Thus, the probability of rolling a one on the first die and a one on the second die is (1/6) * (1/6) = 1/36. Therefore, the probability is 1/36.
To find the probability of rolling a one on the first die and a one on the second die, we need to consider that each die has 6 equally likely outcomes.
Step 1: Calculate the probability of rolling a one on the first die:
Since there is only one outcome that results in rolling a one on a six-sided die, the probability of rolling a one on the first die is 1/6.
Step 2: Calculate the probability of rolling a one on the second die:
Similarly, the probability of rolling a one on the second die is also 1/6.
Step 3: Calculate the probability of both events happening:
To find the probability of two independent events occurring together, we multiply their individual probabilities. Thus, the probability of rolling a one on both dice is (1/6) * (1/6) = 1/36.
Therefore, the probability of rolling a one on the first die and a one on the second die is 1/36.
To find the probability of rolling a one on the first die and a one on the second die, we need to know the total number of possible outcomes and the number of favorable outcomes.
Explanation:
1. Total number of possible outcomes: When rolling two fair six-sided dice, each die has six possible outcomes (numbers 1 to 6). Therefore, the total number of possible outcomes when rolling two dice is 6 * 6 = 36.
2. Number of favorable outcomes: We are interested in the outcome where both dice show a one. There is only one way this can happen. So the number of favorable outcomes is 1.
Now, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 36
Therefore, the probability of rolling a one on the first die and a one on the second die is 1/36.