The positions on a lacrosse team are called defenders (D), midfielders (M), and attackers (A). One player is chosen at random to lead the team in exercises before each game. The letters MDD mean that a midfielder was chosen at the first game and a defender was chosen at the next two
games. The list of all possible outcomes is shown, where each outcome has equal probability of occurring.
AAA AMA ADA
MAA
MDA DAA DMA DDA
AAM AMM ADM MAM MMM MDM
DMM DDM
AAD AMD ADD MAD MMD MDD DAD DMD DDD
MMA
DAM
What is the probability that a defender is chosen at least once, given that a midfielder is chosen at the first game?