Mateus Coelho

 A startup has 6 founders at a strategy retreat. Each pair of founders independently has a one-on-one strategy conversation with probability  1/2 . Question: What is the probability that the final conversation network has exactly 4 links ? A. 1001 32768​   B. 1365 32768 C. 1820 32768 D. 3003 32768​ E. 5005 32768 \frac{5005}{32768} ​

 A data center has 10 backup servers . Each pair of servers can establish a direct synchronization link independently with probability  1/9 . Question: Which statement is correct about this network? A. The expected degree is 8/9 , so the network is below the critical point. B. The expected degree is 1 1 , so the network is exactly at the critical point. C. The expected degree is 10/9 10/9 , so the network is above the critical point. D. The expected number of links is 10 , so the network is above the critical point. E. The expected degree is 2, so the network is far above the critical point.

 A conference app is used by 9 attendees . Each pair of attendees connects independently with probability  1 / 4 . Question: What is the expected number of connections in this network? A. 7 B. 8 C. 9 D. 10 E. 12