The spinner below has 6 equal colored regions numbered 1-6. Find the probability of stopping on yellow for the first spin, stopping on an even number on the second spin, and stopping on blue or red on the third spin.

this problem, what we're told that the spinner below has 6 equal colored regions. We have 2 red regions, 2 blue regions, and 2 yellow regions. Now these regions are also numbered 1 through 6 going around clockwise. Now we wanna find the probability of stopping on yellow for the first spin, stopping on an even number for the second spin, and stopping on blue or red of the 3rd spin. So now we have 3 different events happening here, but all of these events are independent each other. We're having 3 separate spins. What happens on one spin doesn't affect what's going to happen on any of the others. So here, to find the probability of these three events happening, the probability of a and b and C occurring, we're simply going to multiply all of their probabilities together. So the probability of A times the probability of B times the probability of c. Now I'm gonna go ahead and label these events a, b, and c. Of course, you don't have to call events a, b, and c. You can always refer to them as what they specifically are. For example, finding the probability of yellow, I could just write p of yellow. But here, I'm gonna go ahead and identify what all of these events are so that I can keep it a bit more simple. So looking in my problem here, the first event that I have is stopping on yellow for the first spin. So I'm going to refer to this as event a. Then for my second event, I have stopping on an even number for that second spin, so I'm going to refer to this as event b. Then I have one final event here, stopping on blue or red on that 3rd spin, and I'm going to refer to this as on blue or red on that 3rd spin, and I'm going to refer to this as event c. So we want to look at each of these individual probabilities before we get to our formula, multiplying all of them together. So first, looking at the probability of a. So we them together. So first looking at the probability of a. So we have event a as getting yellow on the first spin. So the numbers don't really matter to me at all here. I'm just looking at the colors. Now I have 2 yellow regions out of a total of 6 different regions, so I know that I have a 2 in 6 chance of landing on that yellow. Now we can move on on to event b. So for the probability of b, this one is a bit more complicated because it has stopping on an even number. So now we need to consider what numbers we're dealing with here. Now to spin an even number, I wanna land on either 2, 4, or 6. Those are the only 3 possible even numbers. And there are 3 of those out of a total of 6 different regions here. So I know that I have a 3 in 6 chance of landing on an even number. Then we have one final event, event c, which is stopping on blue or red. So looking at this, I wanna look at which regions are blue or red. I have 2 blue regions, and I have 2 red regions. So I have a total of 4 different things that would satisfy this event here. So I know that the probability of event c is 4 over 6. So since I have all of these individual probabilities, now all that's left is to plug them into my formula and multiply them all together. So I'm going to take twosix, multiply it by threesix, and finally by 4 6ths. Now multiplying all of that across, I end up with 24 on the top in that numerator divided by 216. So out of 200 possible outcomes, only 24 of them would be event a and b and c occurring. But as a decimal, this could be expressed as 0.11. So the probability of getting yellow on that first spin, an even number on the second spin, and stopping on blue or red on that third spin is 0.11. Thanks for watching and let me know if you have questions.