Sara and Tom have just met, and wonder whether they have mutual friends. Each has 50 friends, out of 1,000 other people who live in their town. They think that it's unlikely that they have a friend in...

What is the expected number of mutual friends Sara and Tom have?

Extracted text: Sara and Tom have just met, and wonder whether they have mutual friends. Each has 50 friends, out of 1,000 other people who live in their town. They think that it's unlikely that they have a friend in common, saying "each of us is only friends with 5% of the people here, so it would be very unlikely that our two 5%'s overlap." Assume that Sara's 50 friends are a random sample of the 1000 people (i.e., equally likely to be any 50 of the 1000), and similarly for Tom. Also assume that knowing who Sara's friends are gives no information about who Tom's friends are. What is the expected number of mutual friends Sara and Tom have? Hint: You may consider creating an indicator random variable for each person in their town.