+738 Hi Guest!
This problem was super hard but after a while I figured it out :)
So, Kendra can move right, left, down or up on the game board. We are asked to find the probability that the sum of the numbers in the
spaces on which he will land will be exactly 30 after her third complete turn. There are 4 different ways you can go at each turn or 4 × 4 × 4 = 64 combinations. How many combinations sum to 30? We can do it either with 10 + 10 + 10, or 10 + 5 + 15 because getting to a 20 takes at least 4 turns. To get 10 + 5 + 15 we can go: RRU; RRD; LLU or LLD. That’s 4 combinations.
(R = right, U = up, D = down, L = left)
To get 10 + 10 + 10, look at one scenario first (first move up): URD; URL; ULD; ULR. Four similar patterns emerge with a first move of
R, D or L. This gives us a total of 16 combinations for 10 + 10 + 10.16 + 4 = 20 total combinations.
So, the answer is \(\frac{20}{64}=\boxed{\frac{5}{16}}.\)
