Jack and Jill play a dice game where they roll a die. Jack wins if the number he rolls is higher than Jill's. Jill wins if the number she rolls is higher than Jack's. If both of them roll the same number, Jill wins.
a) Jack rolls his die twice and notes the higher of the two numbers while Jill only rolls her die once. What is the probability that Jack will win?
b) Find a general formula for the probability that Jack will win if both Jack and Jill roll the die multiple times and note the highest number rolled