 Hello everyone, this is Alice Gao. In this video, I'm going to discuss two questions in lecture 5 on slides 27 and 28. The correct answer to question 1 is B. As the temperature decreases, the probability of moving to a worse neighbor decreases. The correct answer to question number 2 is B as well, as the cost difference delta C increases, the probability of moving to a worse neighbor decreases. The intuition for both answers are similar. Moving to a worse neighbor is a risky move. As the temperature decreases, we want to take fewer risks. Therefore, it makes sense to decrease the probability of moving to a worse neighbor. Similarly, as the neighbor becomes worse, it becomes riskier to move to the neighbor. After all, our goal is to minimize the cost of the current state. Therefore, it makes sense to decrease the probability of moving to the neighbor. Let me solve the first question mathematically. The cost difference delta C is positive and the temperature T is positive. Therefore, the fraction delta C divided by T is positive. As T decreases, the fraction increases. Then the exponent, which is the negative of the fraction, becomes more negative and decreases. Therefore, the probability decreases since the exponential function is increasing. You can also solve this by trying some numbers. Let's fix delta C to be 10. If T decreases from 100 to 10, then the probability also decreases from 0.9 to 0.36. Similarly, we can also solve question 2 mathematically. Delta C is positive, T is positive. Therefore, the fraction delta C divided by T is positive. If we increase delta C, then the fraction delta C divided by T increases. The exponent, which is the negative of the fraction, decreases. So the probability decreases because the exponential function is an increasing function. We can also solve this by trying some numbers. Let's fix the temperature to be 10. Then if we change delta C from 10 to 100, then the probability decreases from 0.36 to 0.00045. Here's the takeaway from these two questions. Moving to a worse neighbor is a risky move. It is a type of exploration. Therefore, as the temperature decreases and as the neighbor becomes worse, we want to explore less. So we want this probability to decrease. That's everything for this video. Thank you for watching and I will see you in another video. Bye for now.