Let's analyze this dice game between Xiao Ming and Xiao Hua. Xiao Ming wins when the die shows an odd number, and Xiao Hua wins when it shows an even number. We need to determine if this game gives both players equal chances of winning.
Let's examine all possible outcomes when rolling a standard six-sided die. The die has faces numbered 1 through 6. The odd numbers are 1, 3, and 5, which would make Xiao Ming win. The even numbers are 2, 4, and 6, which would make Xiao Hua win. Each face has an equal probability of 1/6 of appearing.
Now let's calculate the probabilities. For Xiao Ming to win, the die must show an odd number. There are 3 odd numbers out of 6 total outcomes, so his probability is 3 divided by 6, which equals one half. For Xiao Hua to win, the die must show an even number. There are also 3 even numbers out of 6 total outcomes, so her probability is also 3 divided by 6, which equals one half. Both players have exactly the same probability of winning.
To verify our theoretical calculation, let's imagine we simulate rolling the die 1000 times. In such a simulation, we would expect Xiao Ming to win approximately 500 times and Xiao Hua to win approximately 500 times. The bar chart shows these expected results. As we increase the number of rolls, the actual ratio gets closer and closer to the theoretical 50-50 split, confirming that the game is indeed fair.
In conclusion, yes, this dice game between Xiao Ming and Xiao Hua is completely fair. The reason is that both players have exactly equal chances of winning. There are three odd numbers and three even numbers on a standard die, giving each player a 50% probability of winning on any single roll. Since neither player has an advantage over the other, this game meets the definition of a fair game where all participants have equal opportunities to win.