Final answer:
To find the probability that the sum of three cards is greater than a certain value, we need to consider the total number of possible outcomes and the number of favorable outcomes. We can calculate the probability by determining the number of favorable outcomes and dividing it by the total number of possible outcomes. Let's assume the certain value is X. The maximum possible sum we can get from three cards is 39.
Step-by-step explanation:
To find the probability that the sum of three cards is greater than a certain value, we need to consider the total number of possible outcomes and the number of favorable outcomes. Let's assume the certain value is X.
In a standard deck of 52 cards, each card has a value from 1 to 13. The maximum sum we can get from three cards is 13+13+13=39.
Therefore, if X is greater than 39, the probability will be 0. If X is less than or equal to 39, we can calculate the probability by determining the number of favorable outcomes and dividing it by the total number of possible outcomes.
Let's assume that X = 25.
To find the number of favorable outcomes, we need to consider all possible combinations of three cards that add up to a value greater than 25. We can use a systematic approach or list out all the possible combinations to determine this.
Once we have the number of favorable outcomes, we divide it by the total number of possible outcomes, which is the number of ways to choose three cards out of 52.
Finally, we simplify the fraction to get the probability.
For example, if X = 25, one favorable outcome could be drawing the cards 9, 9, and 8.
There are other combinations as well, such as 10, 9, and 6, or 8, 8, and 9. By determining all the favorable outcomes and dividing by the total number of possible outcomes, we can find the probability that the sum of three cards is greater than 25.