Final answer:
The game between Connie and Curtis involves calculating probabilities with two number cubes. Connie scores on an odd sum (18/36 possibilities), and Curtis scores when the sum is 5 or less (10/36 possibilities). A few rolls may not match the theoretical probabilities due to statistical fluctuation.
Step-by-step explanation:
Connie and Curtis are playing a game that involves the probability of rolling two number cubes, and the question is related to understanding those probabilities.
The game's rules state that Connie scores when the sum of the numbers on the cubes is an odd number, and Curtis scores when the sum is 5 or less.
To calculate the probabilities for this game, we would look at all possible outcomes of rolling two six-sided dice. Each die has a 1 in 6 chance of landing on any given number, and since there are two dice, we have a total of 6 x 6 = 36 possible combinations.
For Connie to get a point, the sum of both dice needs to be odd. An odd number can only result from adding an even number to an odd number. Hence, for one die, there are 3 even and 3 odd faces.
Therefore, the number of combinations to get an odd sum is 3 (faces of one die) times 3 (faces of the other die), which equals 9. Since this can happen for either die, we have 9 + 9 = 18 combinations out of 36 that result in an odd sum, giving Connie a chance of 1/2 (or 50%) for each roll.
For Curtis to get a point, the sum must be 5 or less. The possible combinations for this to happen are (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1).
This gives Curtis a total of 10 combinations out of 36, yielding a probability of approximately 27.78% for each roll.
Understanding these probabilities helps in making predictions about the game's outcome over time. If they were to roll the dice only a few times, it is not guaranteed that the actual outcomes will closely match the theoretical probabilities due to the small sample size – an occurrence known as statistical fluctuation.