Die rolling probability with independent events

find the probability of rolling even numbers three times using a six-sided die numbered from 1 to 6 so let's just figure out the probability of rolling at each of the times so the probability of rolling even number so even roll on six-sided six-sided die so let's think about that probability well how many total outcomes are there how many possible rolls could we get well you get one two three four five six and how many of them satisfy these conditions that it's an even number well it could be a two it could be a four or it could be a six so the probability is the events that match what you need your condition for right here so three of the possible events are an even role and it's a out of a total of six possible events out of a total of six possible events so there is a three over six the same thing as one half probability of rolling even on each roll now they're going to roll they want to roll even three times and these are all going to be independent events every time you roll it's not going to affect what happens in the next roll despite what some gamblers might think it has no impact on what happens on the next roll so the probability of rolling even three times so the probability of rolling even three times is equal to the probability of an even roll even roll one time or even roll on six-sided die this thing over here is equal to that thing times times that thing again all right that's our first roll let me copy let me paste it times that thing and then times and then that times that thing again right that's our first roll which is that that's our second roll that's our third roll there independent events so this is going to be equal to one-half that's the same 1/2 right there times 1/2 times 1/2 which is equal to 1 over 8 there's a 1 in 8 there 1 there's a 1 in 8 possibility that you roll even numbers on all three rolls on this roll this role and that role