two dice are rolled. what is probability of rolling a 2 and a 3?
There are a total of 36 possible outcomes when rolling two dice (6 possible outcomes for the first dice and 6 possible outcomes for the second dice).
The possible outcomes for getting a 2 on the first dice are (1, 2) and (2, 1).
The possible outcomes for getting a 3 on the second dice are (1, 2), (2, 1), and (3, 0).
Since (1, 2) and (2, 1) are common outcomes for both getting a 2 and a 3, we count this outcome only once.
Thus, the total number of favorable outcomes is 1.
Therefore, the probability of rolling a 2 and a 3 is 1/36.
To calculate the probability of rolling a 2 and a 3 with two dice, we need to determine the number of ways the outcome can occur and divide it by the total number of possible outcomes.
Since each die has 6 sides with numbers from 1 to 6, there are 6 possible outcomes for the first die and 6 possible outcomes for the second die, resulting in a total of 6 x 6 = 36 possible outcomes.
To roll a 2 and a 3, only one combination is possible: the first die rolls a 2 and the second die rolls a 3. So, there is 1 favorable outcome.
Therefore, the probability of rolling a 2 and a 3 is 1/36 or approximately 0.028, which can be written as a percentage as approximately 2.8%.
To find the probability of rolling a specific combination of numbers on two dice, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Each die has six sides, numbered from 1 to 6. Hence, the total number of outcomes when rolling two dice can be calculated by multiplying the number of sides for each die. Thus, there are 6 * 6 = 36 possible outcomes when rolling two dice.
To determine the number of favorable outcomes for rolling a 2 and a 3, we need to count how many times we can obtain a 2 and a 3. Since the two dice are distinct, we can obtain a 2 and a 3 in two ways: (2, 3) and (3, 2).
Therefore, the number of favorable outcomes is 2.
To calculate the probability, we divide the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 2 / 36
Simplifying further, the probability of rolling a 2 and a 3 is 1/18 or approximately 0.056 (rounded to three decimal places).