A single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 4 the second time.
To find the probability of both events happening, we need to multiply the probabilities of each event occurring.
For the first roll, there are 6 equally likely outcomes since there are 6 sides on the die. Out of these 6 outcomes, half of them are even numbers (2, 4, 6) and the other half are odd numbers (1, 3, 5). Therefore, the probability of rolling an even number on the first roll is 1/2.
For the second roll, again there are 6 equally likely outcomes. Out of these 6 outcomes, only 2 of them are greater than 4 (5 and 6). Therefore, the probability of rolling a number greater than 4 on the second roll is 2/6, which simplifies to 1/3.
To find the probability of both events occurring, we multiply the probabilities:
P(even number on first roll) * P(number greater than 4 on second roll) = (1/2) * (1/3) = 1/6
Therefore, the probability of rolling an even number on the first roll and a number greater than 4 on the second roll is 1/6.