A box contains tiles, numbered 1, 2, 3,..., 49, 50. Only tiles which are marked with a number congruent to 2 mod 8 are blue. One tile is chosen randomly from the box. What is the probability that the tile is blue?
All numbers congruent to 2 mod 8 will be equal to 2 plus or minus some multiple of 8.
Therefore in the range given of numbers 1 through 50, the tiles with the following numbers will be blue: 2,10,18,26,34,42,50.
Therefore there are 7 blue tiles in the box of 50 tiles.
The probability of randomly choosing a blue tile is 7/50 = 14%