What is the probability of rolling an odd number on a number cube containing numbers 1 through 6

 Probability of rolling an odd number is 3/6

1/2

odd numbers: 1,3,5 (total of three)
even numbers: 2,4,6 (also three)
total possible outcomes: 6
3/6 probability of being odd
3/6 probability of being even
(both can reduce by a factor of three to become 1/2)

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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