Final answer:
The probability of drawing a card divisible by 2 or 3 is 8/13. The probability of drawing a square number is 2/13. We calculate these by dividing the number of favorable outcomes by the total number of possible outcomes in the sample space.
Step-by-step explanation:
To solve for the probability that the card drawn bears a number divisible by 2 or 3, and a square number, we first determine the sample space and the favorable outcomes.
- Sample space: The numbers on the cards range from 3 to 15, giving us a total of 13 different numbers.
- Divisible by 2 or 3: The numbers that are divisible by 2 are 4, 6, 8, 10, 12, 14, and those divisible by 3 are 3, 6, 9, 12, 15. Since 6 and 12 are both divisible by 2 and 3, we must avoid counting them twice. There are 8 unique numbers that meet the criteria.
- We calculate the probability as the number of favorable outcomes (8) divided by the total number of possible outcomes (13), giving us 8/13.
- Square numbers: The square numbers within the range are 4 (2²) and 9 (3²), giving us 2 favorable outcomes.
- For the probability of drawing a square number, we again divide the number of favorable outcomes (2) by the total possible outcomes (13), resulting in 2/13.