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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

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