Final answer:
The probability that a Little League team wins all four games is 0.1296, loses all games is 0.0256, wins at least one game is 0.9744, and loses at least one game is 0.8704, when the probability of winning each game is 0.6.
Step-by-step explanation:
The question involves calculating probabilities for a Little League team playing four games, with the probability of winning each game being 0.6.
(a) Win all games:
The probability that they win all of the games is the product of the probabilities of winning each game since each game is independent. So it is 0.6 × 0.6 × 0.6 × 0.6 = 0.1296.
(b) Lose all games:
The probability of losing one game is 1 - 0.6 = 0.4. Therefore, the probability they lose all of the games is 0.4 × 0.4 × 0.4 × 0.4 = 0.0256.
(c) Win at least one game:
The probability of winning at least one game is the complement of losing all games, which is 1 - 0.0256 = 0.9744.
(d) Lose at least one game:
Similarly, the probability they lose at least one game is the complement of winning all games, which is 1 - 0.1296 = 0.8704.
Selecting the appropriate multiple-choice answer (MCQ answer) for each of these probabilities is not provided, but the calculations indicate the theoretical probabilities for these outcomes based on the given probability of winning a single game.