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# probability question

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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 2, Jane wins. Otherwise, her brother wins. What is the probability that Jane wins? Express your answer as a common fraction.

Dec 26, 2020

#1
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The probability is 3/10.

Dec 26, 2020
#2
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All of the pairs of spins have the probability of $$\left(\dfrac 1 5\right)^2 = \dfrac{1}{25}$$.

So all we have do is to count the number of spin pairs where Jane wins and divide it by $$25$$.

List them out. If I correctly understand what "non-negative difference" means, Jane wins with $$(5,5), (5,4), (5,3), (4,5), (4,4), (4,3), (4,2), (3,5), (3,4), (3,3), (3,2), (3,1), (2,4), (2,3), (2,2), (2,1), (1,3), (1,2), (1,1)$$.

Which becomes 19 spin combos that lead to Jane winning.

Therefore, $$P[\text{Jane wins}]=\dfrac{19}{25}$$.

Dec 28, 2020