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MathNet 2012 Question 49

Math Olympiad Vault · MathNet 2012

Question 49

Tilen rolled a die. In a table he recorded the number of rolls for each number of dots:
Number of dots: $1,2,3,4,5,6$.
Corresponding counts: $3(x-2),2x,2(x-1),x+2,2x+1,x$.
(a) How many times did each face occur if the number of sixes is exactly $10\%$ of all rolls?
(b) Calculate the average number of dots.
(c) Draw a frequency pie chart.
(6 points)