To determine how many of the 15 rolls should theoretically result in a number less than 5, we start by recognizing the possible outcomes when rolling a standard six-sided die. The numbers on the die are 1, 2, 3, 4, 5, and 6.
The numbers less than 5 are 1, 2, 3, and 4. This gives us 4 favorable outcomes out of a total of 6 possible outcomes.
To find the probability of rolling a number less than 5, we calculate:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{6} = \frac{2}{3} \]
Next, we want to determine how many of the 15 rolls should theoretically produce a number less than 5. We multiply the total number of rolls by the probability of rolling a number less than 5:
\[ \text{Expected number of rolls} = \text{Total rolls} \times \text{Probability} = 15 \times \frac{2}{3} = 10 \]
Therefore, theoretically, 10 of the 15 rolls should result in a number less than 5.
The correct response is 10.