you roll 2 dice. what is the probability the first die will be an even number and the second die will be a number greater than 4?
To find the probability of both events happening, we need to find the probability of each event individually and then multiply them together.
First, let's find the probability of the first die being an even number.
There are 6 possible outcomes when rolling a six-sided die, and half of them are even numbers: 2, 4, and 6. Therefore, the probability of the first die being an even number is 3/6 or 1/2.
Now let's find the probability of the second die being a number greater than 4.
Again, there are 6 possible outcomes when rolling a six-sided die, and only two of them are greater than 4: 5 and 6. Therefore, the probability of the second die being a number greater than 4 is 2/6 or 1/3.
To find the probability of both events happening, we multiply the probabilities together:
(1/2) * (1/3) = 1/6
So the probability of the first die being an even number and the second die being a number greater than 4 is 1/6.