Today Aiden and I discussed probabilities of compound events (more than one event occurring at the same time). We practiced writing out the sample space of compound events. For example, flipping a coin twice: HH, HT, TH, HT. We discussed how since there are 2 events with 2 possible outcomes, we have 2*2=4 possible outcomes. However if we flipped the coin 3 times we would have the sample space: HHH,HHT, HTH, HHT, TTT, THT, TTH, THH. We get that from 2*2*2=8 possible outcomes. I showed Aiden 3 ways of organizing this data, the sample space shown above, a table, or a tree. Once Aiden was comfortable considering the sample space of compound events, we then considered the likelihood of certain outcomes. For example: if we flip a coin and roll a die there would be 2*6=12 possible outcomes (like H1, T1, H2, T2, H3, etc.) therefore the probability of any outcome like P(T4)=1/12. Aiden has been doing well with this new material, though he doesn’t have a lot of confidence with it yet. He says things like, “I wouldn’t have gotten that if you didn’t tell me. But I should have.” And I respond with, “That’s not true. You would have eventually gotten it. But also this is the first time you’ve ever done this. So you can’t expect yourself to know what to do before you’ve learned it. That’s what I’m here for. And you’re doing great.”