Suppose , On Studying the sample of 10000 random profiles in FB , the count of friends is found as ~N( a1,v1).

For any profile , the % distribution of friends from the same county follows ~N(a2,v2)

1 What sort of distribution would the count of mutual friends of two random profiles  would follow ?

2 What sort of distribution would the count of mutual friends would follow , if  both the random profiles are from same county?

3 What sort of distribution would the count of mutual friends would follow , if  both the random profiles are from different county?

if A sample of 100 pairs for random profiles  is taken,

4 what is the probability that no pair would have more than 7 mutual friends ?

5 what is the probability that  at least 7 pairs would have more than 0 mutual friends ?

6 what is the probability that  at least 7 pairs would have at least  3 mutual friends ?