Final answer:
The probability that Liza wins exactly two times out of 9 games is approximately 0.389.
Step-by-step explanation:
The odds of winning a game at the carnival are 3 in 7, which translates to a probability of 3/7. To find the probability that Liza wins exactly two times out of 9 games, we can use the binomial probability formula. The formula is P(x) = (nCx) * (p^x) * (q^(n-x)), where n is the number of trials (9), x is the number of successes (2), p is the probability of success (3/7), and q is the probability of failure (1 - p). Plugging in the values, we get P(2) = (9C2) * ((3/7)^2) * ((4/7)^7) = 36 * (9/49) * (16384/2401) ≈ 0.389. Therefore, the probability that Liza wins exactly two times out of 9 games is approximately 0.389.