the prime minister of britain is

a. popularly elected
b. the leader of the majority party in the house of commons
c. appointed by the president
b

http://en.wikipedia.org/wiki/Prime_Minister_of_the_United_Kingdom

The correct answer is b. The prime minister of Britain is the leader of the majority party in the House of Commons.

To arrive at this answer, you can apply a basic understanding of the political system in Britain. Here's how you can explain it:

1. Start with the basics: The prime minister is the head of government in Britain.
2. Explain the House of Commons: The House of Commons is the lower house of the Parliament of the United Kingdom.
3. Describe the majority party: The majority party in the House of Commons refers to the political party that has the highest number of elected Members of Parliament (MPs) in the House of Commons.
4. Connect the dots: The prime minister is typically the leader of the majority party in the House of Commons. This means that if a political party gains the most seats in an election, their leader becomes the prime minister.

Therefore, when asked about the prime minister of Britain, the correct answer is "b. the leader of the majority party in the House of Commons."