Algebraic Structure

I would love to have a usual word format answer with detailed proofs. The problems are 6 in total, the numbers are: from attached page #1: #2.82; 2.86; 2.87, from attached page #2: # 2.97; 2.98; 2.99. Thanks in advance. The student.

Tree diagram

The Knicks won the first game against the Lakers in a basketball playoff .If the first team to win four games is the winner, construct a tree diagram for this playoff. Hint: Some of the branches in the tree diagram will end sooner than the other , as one of the teams would have one four games.

Probability

Use a tree diagram. Use a diagram to list the sample space showing possible arrangements of heads and tails when four coins are tossed . Then use the sample space to find the probability that: 1. at most two coins come up heads 2. at least two coins come up heads 3. no more than three coins come up tails.