Final answer:
The child can expect to win 22 times when playing 110 carnival games, as they have a 1 in 5 chance of winning each game.
Step-by-step explanation:
If a child playing a carnival game will be a winner one out of five times, we can say that the probability of winning any single game is 1/5 or 0.20 (which is 20%). To find out how many times the child can expect to win if he plays 110 games, we multiply the total number of games by the probability of winning one game:
Total expected wins = Total games played × Probability of winning each game
Total expected wins = 110 games × 0.20
Total expected wins = 22
Therefore, the child can expect to win 22 times if he plays 110 games. The correct answer is A) 22.