# 11.4.1. Calculating Probability

Two cards are drawn one after the other from a set of 11 identical cards numbered from 1 to 11 and the drawn card must be returned to the deck before drawing another one. What is the number of the elements in the sample space if the sum of the two numbers is more than 17?

• A15
• B16
• C14
• D6

### Example

Two cards are drawn from a deck of 11 identical cards numbered from 1 to 11, and the first card has to be returned to the deck before the second card is drawn. Determine the number of elements in the sample space if the sum of the two numbers on the drawn cards is more than 17.

### Solution

Since the event is selecting two cards, where the sum of the two cards drawn is more than 17, the sum of the two cards must be 18, 19, 20, 21, or 22. To get a sum of 18, the two cards can be 7 and 11, 8 and 10, 9 and 9, 10 and 8, or 11 and 7. To get a sum of 19, the two cards can be 8 and 11, 9 and 10, 10 and 9, or 11 and 8. To get a sum of 20, the two cards can be 9 and 11, 10 and 10, or 11 and 9. To get a sum of 21, the two cards can be 10 and 11 or 11 and 10. Finally, to get a sum of 22, the two cards must be 11 and 11.

This means that the set represents the event.

Thus, the number of elements in the set that represents the event is 15.

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