Q8: On a Friday, the probability of partying is 14. Given that it is Friday, the probability of partying till 3 am is 1/3. Given that it is not Friday, the probability of partying is 1/2. If it's Friday and partying till 3 am, people feel lazy the next day with a probability of 1/4. On the other hand, the probability of feeling lazy the next day is reduced to 1/10 if it is not Friday and there is no partying till 3 am. In other situations (Friday and no partying, not Friday and partying ) the probability of feeling lazy the next day is 1/5. You pick a random day. What is the probability that it's not Friday and there is partying till 3 am and people don't feel lazy the next day? What is the probability that people are feeling lazy the next day? ii) Given that people feel lazy the next day, what is the probability that there was a party on that Friday? ili Given that there is partying till 3 am, what is the probability that it was Friday partying that day? iv Given that it's a Friday party, what is the probability of partying till 3 am and not feeling lazy the next day? V) What is the probability of not partying till 3 am? Given that there is partying till 3 am, what is the probability of Friday and not feeling lazy the next day? [Mark: 30]