+296 Jane and her brother each spin this spinner once. The spinner has five congruent sectors. If the non-negative difference of their numbers is less than 3, Jane wins. Otherwise, her brother wins. What is the probability that Jane wins? Express your answer as a common fraction.
+6251 all pairs of spins have probabilty of \(\left(\dfrac 1 5\right)^2 = \dfrac{1}{25}\)
so we just have to count the number of spin pairs where Jane wins and divide it by 25.
there's no magic to this, just list them out. If I understand what "non-negative difference" means, Jane wins with
(5,5), (5,4), (5,3), (4,5), (4,4), (4,3), (4,2), (3,5), (3,4), (3,3), (3,2), (3,1), (2,4), (2,3), (2,2), (2,1), (1,3), (1,2), (1,1)
i.e. 19 spin combos that lead to Jane winning. Thus
\(P[\text{Jane wins}]=\dfrac{19}{25}\)
