Two number cubes are rolled to determine how a token moves on a game board. The sides of each number cube are numbered 1, 2, 3, 4, 5 and 6.
There are two options describing how the token will be moved.
Option A: If the product is even, move forward 4 spaces. Otherwise, move backward 3.
Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 4.
Use mathematical expectation to determine which option offers the greater likelihood of moving closer to the finish line on the game board.
Let p be the probability of an even roll.
For option A
E[moves]=4p - 3(1-p) = 7p-3
For option B
E[moves]=5p-4(1-p) = 9p-4
Playing with the numbers it turns out that p=P[even roll]=3/4
I suggest you confirm this for yourself.
EA=21/4 - 12/4 = 9/4
EB = 27/4 - 16/4 = 11/4
EB offers the greater likelihood of moving closer to the finish line.