A teacher reaches into a bag of game pieces containing 5 black pieces, 3 purple pieces, 1 orange piece, and 6 green pieces. He draws 2 pieces, setting aside the first piece before drawing the second. What is the probability that at least one of the drawn pieces is purple

The probability of choosing a purple piece is 3/15, choosing an orange piece will be 1/15, that of black pieces is 5/15 and that of choosing a green piece is 6/15.

This would be PP + PW + PG + PB + WP + GP + BP

= (3/15 * 2/14) + (3/15*1/14) + (3/15*6/14) + (3/15+5/14) + (1/15*3/14) + (6/15 * 3/14) + (5/15 * 3/14)

= 6/210 + 3/210 + 18/210+15/210+3/210 + 18/210 + 15/210

= 78/210

= 13/35