To find the most likely number of wins when playing a game with a 69% probability of winning, you can use the binomial probability distribution. In this case, you want to determine the number of successful outcomes (wins) when playing the game 132 times.
The formula for the expected value (or mean) of a binomial distribution is:
Expected Value (μ) = n * p
Where:
n is the number of trials (132 games in this case).
p is the probability of success in a single trial (0.69, or 69%).
Expected Value (μ) = 132 * 0.69 = 91.08
The most likely number of wins is the expected value rounded to the nearest whole number, which in this case is approximately 91 wins. So, the most likely number of wins when playing the game 132 times is 91.