A single die is rolled twice. Find the probability of getting a 2 the first time and a 3 the second time
To find the probability of getting a 2 on the first roll and a 3 on the second roll of a fair six-sided die, we calculate the probability of each individual event and then multiply them, because the rolls are independent events.
The probability of rolling a 2 on a six-sided die for the first roll can be calculated as follows:
- There is 1 favorable outcome (rolling a 2) out of 6 possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
- So, the probability P(2) = 1/6.
The probability of rolling a 3 on the second roll is similarly calculated:
- There is 1 favorable outcome (rolling a 3) out of 6 possible outcomes.
- So, the probability P(3) = 1/6.
Since each roll of the die is independent, the probability of both events happening in sequence (rolling a 2 first and then a 3) is the product of their probabilities:
- P(2 first, then 3) = P(2) * P(3) = (1/6) * (1/6) = 1/36.
Thus, the probability of rolling a 2 on the first roll and a 3 on the second roll of a fair six-sided die is 1/36.