The probability of a person winning a game is 0.8, the probability of him losing a game is
P (winning a game) = 0.8
Winning or losing a game are complementary events.
Also, for complementary events, P(A) + P(¯¯¯¯A) = 1.
Because the sum of probabilities of an event and its complementary event is always 1.
⇒ P(winning a game) + P(losing a game) = 1
Then, P(losing a game) = 1 - P(winning a game) = 1 - 0.8
⇒ P(losing a game) = 0.2
Therefore, the probability of losing a game is 0.2.