The spinner below has 6 equal regions. Find the probability of landing on yellow for the first spin and not landing on yellow on the second spin.

In this problem, we're told that the spinner below has 6 equal regions. We see that it has 2 red regions, 2 blue regions, and 2 yellow regions. And we wanna find the probability of landing on yellow for the 1st spin and not landing on yellow for the 2nd spin. Now here we have 2 independent events because the outcome of 1 does not affect the outcome of the other. So here we want to find the probability of event a and event b happening, which we know we can do by multiplying our probabilities together. So we know that we can find the probability of A and B by multiplying the probability of A times the probability of b. So we need to first find the probabilities of each of these individual events. So looking at my very first event, it is landing on yellow for the first spin. So I'm going to refer to this as event a. Then for event b, we have not landing on yellow for the second spin. So this is our second event, event b. Now when considering the probability of a, since there are 2 yellow regions out of a total of 6, we know that there is a 2 over 6 probability of landing on yellow on that first spin. Then for our 2nd spin, we're looking at the probability of not landing on yellow. So for the probability of b, since I'm looking for all of the regions that are not yellow, I have these 2 blue regions and I have these 2 red regions, that gives me 4 out of my total 6 regions. So the probability of not landing on yellow on that second spin is 4 over 6. Now that I have my individual probabilities here, I can go ahead and just plug them into my formula and multiply them together to get the probability of a and b. So here, I'm going to take 2 6ths and then multiply it by 4 6ths. And multiplying across here, I get 8 over 36. Now this simplifies as a fraction to 2 9ths, and as a decimal, you will get 0.22. So the probability of landing on yellow on the 1st spin and not landing on yellow on the 2nd spin is 0.22. Thanks for watching and let me know if you have questions.