Suppose You and a Friend Each Choose at Random an Integer

Short Answer

Suppose you and a friend each choose at random an integer between 1 and 8, inclusive. For example, some
possibilities are (3, 7), (7, 3), (4, 4), (8, 1), where your number is written first and your friend's number second.
Find the following probabilities: (a) $p ($ you pick 5 and your friend picks $8 )$ .
(b) $p$ (sum of the two numbers picked is $< 4$ ).
(c) $p$ (both numbers match).
(d) $p$ (the sum of the two numbers is a prime).
(e) $p$ (your number is greater than your friend's number).